Callum Wilson scored a late equaliser after a goalmouth scramble to earn Bournemouth a point in a South Coast thriller.
Anthony Knockaert scored the first Premier League goal of 2018 when he converted a cross from Ezequiel Izquierdo after only four and 32 seconds.
Steve Cook equalised after 33 minutes with a towering header from a Jordan Ibe corner.
Brighton seemed set for only their second win in 11 games when Glenn Murray gave them the lead again after 48 minutes when he slotted home against his old club after another Izquierdo assist.
But the Colombian failed to seal the three points when Asmir Begovic saved his effort when he was clean through.
And Brighton were made to pay after 79 minutes when they repeatedly failed to clear another Ibe corner and Wilson prodded the loose ball past a wrong-footed Mathew Ryan.
Both keepers made a string of quality saves in an open, entertaining game.Wilson was also denied two potential penalties when he was caught by Shane Duffy in the first half and then pushed by Ezequiel Schelotto in the box after the break.
The draw denied Seagulls manager Chris Hughton a win to celebrate his third anniversary in charge of the club after taking over with the club 21st in the Championship on December 31 2014.
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How they line up
Cherries' Cook out to beat former club
Bournemouth defender Steve Cook says he has “no axe to grind” with Brighton – but still dreams of scoring the winning goal against them.
Cook, 26, began his career with the Seagulls, but fled to their south-coast neighbours in 2012 after making just one league start.
The centre-back, who returns to the Amex as a Premier League player for the first time today, said: “I am desperate to go back there and win.
“I am delighted for Brighton and have no axe to grind. I didn’t leave because I got shunted out the door.
“I chose to leave and it was a decision I am delighted I made. But it is a game we have to win. We could be playing anyone away and I’d say the same. I am desperate to win any game and we have not won enough.
“It would be nice to go back to my old club and get a win.
“The dream is for me to score the winner, but right now I’d take anyone scoring, or three own goals, I am just so desperate to win.”
Cook remains close pals with Brighton defender Lewis Dunk and is backing him to one day star for England.
He added: “I spoke to Lewis over Christmas and will speak to him just before (the match), and maybe see him. He is a good mate but hopefully I will get one over him.
“Why can’t he get in the England squad? He is a very good defender and a very good player.
“I am sure he will have his eyes set on that, but that is down to him. If he keeps playing well and keeping clean sheets (I’m sure he’ll be given a chance).
“Brighton are a very defensive side. That is how they play so that helps him.”
The Cherries dragged themselves out of the Premier League’s bottom three on Saturday, by beating Everton 2-1, to end an eight-match run without a win.
Cook insists Eddie Howe’s men are not feeling the strain, adding: “We are just over halfway through the season, so the pressure has not started yet.
“These are enjoyable games, the games we want to be playing in, and there is plenty more football to be played.
“This isn’t pressure, this is football, and we are still enjoying it.
“But we are not happy – wins will make us happy and I am sure they will come.”