Subs Josh King and Lys Mousset scored second-half goals to hand Paul Lambert his first defeat as Stoke manager.
Just three days after shocking Chelsea at Stamford Bridge, the Cherries had seemed set for their first loss of 2018 when Xherdan Shaqiri headed home a cross from new signing Badou Ndiaye after only five minutes.
Eddie Howe had sent out the same starting 11 as in midweek and King only came on after 13 minutes when Steve Cook limped off injured. The Norwegian striker set up his a 35th-minute chance for Jordan Ibe but Erik Pieters made a wonder block on the line.
King was booked by referee Paul Tierney for diving in the second half before taking advantage of confusion between Joe Alle and Kurt Zouma to equalise after 71 minutes.
It King's first goal for the Cherries since November – and the first Stoke had conceded under Lambert in his third game in charge.
And then Mousset, who came on after 59 minutes, scored the winner 19 minutes later when he headed home Ibe's free kick but declined to celebrate.
Bournemouth are now undefeated in seven matches since Christmas.
Peter Crouch had headed against the corner of post and bar from a Shaqiri corner after 65 minutes when Stoke were still leading.
Lambert rallies Stoke strikers
Stoke manager Paul Lambert wants his goal-shy strikers to give him a selection dilemma as he looks to steer the club away from the Premier League relegation battle.
The Potters have scored 25 goals in 25 league games this season, with Mame Biram Diouf the top scorer with five, and find themselves just a point above the relegation places.
Diouf went nine games without a goal in all competitions before scoring in the 2-0 win over Huddersfield last month and Lambert will look for fellow strikers Peter Crouch and Saido Berahino to shoulder some of the goalscoring burden.
“I think Mame gives us something different to what we have and he has obviously started the last couple of games, and scored a goal too,” Lambert told a pre-match press conference ahead of the trip to Bournemouth, who enjoyed a 3-0 win at Chelsea on Wednesday.
“That said, Peter came on in midweek [in the 0-0 draw with Watford] and changed the game in our favour, so he is a very good option for us too. Saido Berahino is a fantastic finisher too, I have seen that in training, and if he can get a little bit fitter then he is somebody who can have a real impact.
“In terms of quality, he has it, and so do the other guys. We just need the three of them firing, giving me selection headaches.”
Defender Moritz Bauer has helped Stoke keep two clean sheets in the three appearances he has made since his January move from Rubin Kazan and is determined to maintain his impressive start to life at the club.
“It is vitally important that we get enough points to stay in the Premier League, and with the quality we have, and a great manager, I really believe we will do that,” Bauer told the club’s website.
“It is going to be difficult though because there are many teams in a situation like ourselves, so we have to do all we can to make sure that we finish the season in a strong position.”