Alexis Sanchez has put the Gunners in the box seat in extra time after tapping in following some sloppy defending by Man City.
In regular time, City striker Sergio Aguero's one-on-one finish against a tentative Petr Cech in the Arsenal goal was cancelled out by Nacho Monreal, wh finished emphatically after a perfect run at the far post.
Aguero's substitution was followed almost immediately with a goal for the north Londoners that could see them return for the final.
Arsenal: Cech, Gabriel, Koscielny, Holding, Oxlade-Chamberlain, Ramsey, Xhaka, Monreal, Ozil, Sanchez, Giroud
Subs: Martinez, Bellerin, Gibbs, Coquelin, Walcott, Iwobi, Welbck
Manchester City: Bravo, Navas, Kompany, Otamendi, Clichy, Toure, Fernandinho, De Bruyne, Silva, Sane, Aguero.
Subs: Caballero, Zabaleta, Fernando, Sterling, Kolarov, Delph, Iheanacho.
Pep Guardiola says defeat was tough on City
Pep Guardiola says that City dominanted the majority of the game and can count themselves unlucky.
“In games like this, you can’t expect to control all the situations but we did most of the time.
“We performed like we would want to in a final. We did absolutely everything. Congratulations to Arsenal. We’ll improve next season. We competed here, we had more chances but the finishing was like it has been throughout the season.
“We played like we wanted to and that’s all. We are sad but tomorrow we have to stand up to finish the games we still have to play.
“I don’t have regrets about the team. We just have to compete in these games. We are here for the results. Next season we will be stronger.”
Arsene Wenger on his decision to play three at the back...
“In this period we needed more security, a bit more defensive stability. The players looked comfortable in the position they were playing.
“It was not only those who scored goals [who played well]. Many people, Ozil has shown again today he can fight. Overall it was a great team performance.”
Asked about his future, Wenger said: “People can question my decision but not my loyalty and commitment to the club.”
More from Arsene Wenger, this time speaking to BT Sport...
“I am very proud of our performance and spirit. I felt we became stronger. In the first half maybe we were a bit cautious, accepting to be dominated, and then we became stronger and stronger. It was a very tight game but overall I think we deserved to win the game.
“We went through a difficult period. I will talk one day about that. I feel players showed great togetherness today.”
Sanchez's performance was important, says Wenger
More from Arsene Wenger and he has been extremely complimentary of the performance of Alexis Sanchez.
“Alexis Sanchez was like the team. He had problems to start and became stronger and stronger. He is an animal, always ready to kill the opponent. He will never give up. He will be here next year because he has a contract and hopefully we will manage to extend him.
“When at Arsenal football club we want the team to turn up in big games and I think we done that today. Overall I am very pleased. People questioned us, we went through tough times. In these times you can be divided or united and today we have shown the right response.”
Arsene Wenger reacts to extra-time win
Wenger has told Match of the Day that he was delighted with his team’s mentality in the FA Cup semi-final win over Manchester City.
“I am very pleased, it was a big game today. Overall it was a great performance not only technically but mentally. We became stronger and in the end deserved to win the game.
“The team performance was there. When the players give their best and are completely focused you always stand up for them.
“We were close to scoring and on the break they are very good. We lost the ball and conceded the goal but we showed the right response.”
Manchester City player ratings
Bravo 6
Plenty of Pep-pleasing fancy footwork but hardly inspired confidence
Navas 6
Always going to struggle defensively and caught out for Monreal goal
Kompany 6
Getting through another 90 minutes will be the big bonus for the skipper
Otamendi 6
A mixture of the tough and the illegal, defended with menace
Clichy 4
Distribution and final ball are way short of top class
Fernandinho 6
Booked. Unlucky to see one meaty header thunder against the crossbar
Toure 6
Booked. Regularly drove forward but years seemed to take their toll
De Bruyne 6
Booked. Form has tapered off, ran down too many blind alleys
Silva 6
Distraught after being kicked out of the game early by Gabriel
Sane 6
Pace always caused problems but often double-marked
Aguero 7
Continued his hot run of scoring form but limped off in extra-time
SUBS
Sterling (Silva 22 mins) 6
Delph (Fernandinho 98 mins) Booked
Fernando (Aguero 98 mins)
Iheanacho (Sterling 106 mins)
Arsenal player ratings
Cech 5
Hesitant all afternoon, never more so than for the Aguero opener
Gabriel 7
Good but most significant contribution was to end Silva’s game early
Koscielny 7
A few crucial interventions and generally led by example
Holding 7
Would never have him down as a rookie on this evidence
Xhaka 5
Customary blend of misplaced passes and mistimed tackles
Oxlade-Chamberlain 8 MOTM
Always looking to make something happen and eventually did
Monreal 7
Toiling until arriving with a sweet finish with his wrong foot
Ramsey 5
Dispossessed once too often and struggling for confidence
Ozil 6
Not his accurate self but could not say he did not put in the graft
Sanchez 7
Booked. Threatened to bring some magic and then in right place at right time
Giroud 5
Never made a mark on proceedings, lucky to last so long
SUBS
Welbeck (Giroud 82 mins) 7
Bellerin (Oxlade-Chamberlain 105 mins)
Coquelin (Ozil 118 mins)
Former Gunner Serge Gnabry was in attendance at Wembley and was delighted to see his mates win.
More Arsenal reaction as Aaron Ramsey talks to BBC Radio 5Live.
“I love this competition. We have been quite successful in recent years and you can see the passion that the players play with. We went behind and kept on going and got a result.
“I made the mistake for the goal. I know in these situations you have to respond. I carried on trying to work my socks off and ultimately it paid off.
“That is the second time we played this formation credit, to the boys. We have shown the character we have in this team.
“It was important to win today, to have something to look forward to. But now we have another seven cup finals to try and get into the top four.
“We have let him [Arsene Wenger] down at times this season, we want to win it for him and ourselves.”
Alex Oxlade-Chamberlain was awarded man of the match and he has been talking to BT Sport.
“I’m tired but delighted. We set out to reach the final, our league form has not been good enough and this is something we could hold on to.
“We have given ourselves every opportunity to go and win it.
“It’s a new and interesting position for me at wing-back, I have to focus on the defensive side of things and we have adapted really well.”
Look how much it meant to Arsene Wenger!
Arsenal use the rough stuff
Laurent Koscielny, Gabriel and Granit Xhaka all got stuck in and boot the boot into Manchester City in a very un-Arsenal sort of way.
You could argue it’s time Arsenal toughened up. It annoyed City who were dominant and frustrated them.
First, Arsenal went to a back three at Middlesbrough (which they stuck to again) and now they are using rough house tactics.
Whatever next?
Reffin' hell
We really should have the best refs for the best games. Craig Pawson is up and coming - but not among the best, in my opinion. Martin Atkinson on Saturday, why not Michael Oliver today?
Pawson and his linesmen made key areas, the worst when Manchester City had a goal wrongly ruled out after Leroy Sane’s cross was judged by linesman Steve Child to have crossed the line before Raheem Sterling put it in. It didn’t go out.
Pawson lost the game when he failed to book Gabriel for a foul on David Silva which ultimately forced the Manchester City midfielder off early.
Then no-one could complain when Pawson didn’t book Vincent Kompany for a foul on Mesut Ozil which also should have been a booking.
Alexis Sanchez was eventually booked for a foul which wasn’t as bad as either of the other two as Pawson tried to play catch up. He’d long since lost authority.
Wembley are trying - and it's working
One of the big criticisms of the new Wembley is a lack of atmosphere (the pitch is actually better these days) but the crowd was fabulous on Saturday and it was good again today.
Slightly manufactured with blue silver foil flags and red and white flags. But they’re trying and, just before kick-off, there was a good noise and atmosphere.
Arsenal dug deep and showed resilience
They have been on such a poor run that you questioned their belief and confidence.
When they went behind it looked really bad, but Arsenal’s gritty performance was for the fans and for their manager.
A really brave, strong performance long into extra time.
Pep's first season has been underwhelming
This must go down as a big disappointment for Pep Guardiola, the manager deemed as the best in the world, the prize catch and he’s ended up potless after his first season.
City are still a work in progress but this must go down as a big disappointment and Guardiola must build his own squad for next season - and improve dramatically.
Short report: Arsenal 2-1 Manchester City (AET)
Alexis Sanchez hit a dramatic extra time winner to put Arsene Wenger on course for FA Cup history.
Arsenal fought back from going a goal down to win a thrilling semi final with a 110th minute tap-in from Sanchez and Wenger is now dreaming of a record seventh FA Cup win.
It broke Manchester City’s hearts as Pep Guardiola’s men will be cursing their luck and near misses which ultimately cost them.
City were desperately unlucky not to be ahead at half time when linesman Steve Child wrongly ruled the ball had gone out before Raheem Sterling put it in the net.
But City took the lead after 62 minutes when Sergio Aguero pounced on some poor Arsenal defending, exposed Monreal and lifted the ball over Petr Cech who was slow off his line.
That looked a devastating blow for Arsenal but Monreal, of all people, made amends by scoring a 71st minute equaliser from Alex Oxlade-Chamberlain’s cross.
City roared back as Yaya Toure and Fernandinho hit the woodwork while Danny Welbeck missed a big chance to stop the game going into extra time.
Stick with us here, we’ll bring you all of the reaction from Wembley, as Arsenal secure their place in the FA Cup final, where they will take on Chelsea in five weeks’ time.
A harsh one on City and Pep Guardiola finishes his first season at Manchester City without a trophy.
PEEP PEEP! FT' Arsenal 2-1 Man City
Arsenal have done it! They will face Chelsea in the FA Cup final in May!
It’s a ninth FA Cup final for manager Arsene Wenger. A much-needed win for him!
Last chance for City. One additional minute.
Change for Arsenal as Ozil is replaced now by Coquelin.
A good shift from Ozil, in fairness. Very good during the second half of regular time.
Wide! Yaya Toure tries to curl an effort but he overhits it and it goes wide of the post.
City are looking increasingly open at the back as they push for an equaliser. Arsenal could yet go on and score a third here.
Three and a half minutes to go, City are moving forward...
It’s all becoming a little bit repetitive now. Balls into the Arsenal box from City but defensive headers clearing the danger.
De Bruyne fires a low effort across goal now and it fires just wide of the far side.
BIG CHANCE!
De Bruyne plays the ball through to Delph but the effort on goal gets a deflection.
That is probably as good of a chance as City can ask for!
Toure had a free-kick on the edge of the box for City but it hit the wall.
Arsenal looked to break in numbers but the quality wasn’t quite there.
That will probably be a theme of these final 10 minutes!