Scott Dann scored first for the Eagles when turning home Wilfried Zaha's rifled cross in the 27th minute.
However, the Cherries responded seven minutes later when Marc Pugh danced around Dann before delivering a perfectly-placed shot inside Wayne Hennessey's far post from just inside the area.
The win saw Eddie Howe's Cherries move up to 15th on the table whereas Alan Pardew's Palace fell to 12th on the back of a fifth straight loss.
- Bournemouth looking like they are good enough to avoid the drop. Will this be a massive achievement from Howe and his men if they can pull it off?
- Problems for Pardew and Palace. They have not won in seven and have scored just two goals during that time.
Palace are in desperate need of a win and will be hoping they can land one at Swansea on Saturday as Bournemouth prepare to host Arsenal on Sunday.
God is good.. What a win tonight. Our fans were outstanding again! Tough game but we did it! #RealMenWearPink#AFCBpic.twitter.com/6nLFb7Lpev
— Benik Afobé (@Afobe_) February 2, 2016
75th career goal and what a result. Lads were different class #Blessed
— Marc Pugh (@MarcPugh7) February 2, 2016
Palace boss Pardew on his side's misfortune:
"We're a bit unlucky to lose, we had some good chances. The two chances they had they go in: that's the run we're on at the moment.
"It is becoming a problem, our strikers not scoring, there's no doubt about that.
"We're going to have to really dig in at Swansea (on Saturday), to try and get something."
Bournemouth's Howe on Afobe who has three goals in his last three games:
"You hope (Afobe will have the impact he has had), I don't know if you expect. He's got time on his side, he's a young player, he's still got a lot of improvement in him.
"He's adapted to the level, the move, the hype. It's been really pleasing that he's had the confidence and temperament to take it in his stride and carry on doing what he was doing for Wolves."
*Thanks to Opta
7 - Scott Dann's goal was Palace's seventh from a defender this season, a PL high. Handy.
— OptaJoe (@OptaJoe) February 2, 2016