The hosts took the lead after just 27 minutes as Scott Dann fired in from close range, but Marc Pugh responded five minutes later by striking into the bottom right corner to level proceedings.
Benik Afobe then adjusted superbly to head home the winner in the second half after Wayne Hennessey parried Matt Ritchie's initial strike into the 22-year-old's path.
It was the Cherries that created the first real chance of the match. Dan Gosling surged forward and was brought down by James McArthur just shy of the home side's penalty area. Andrew Surman then teed up the resulting free kick for Ritchie to have a go at, but his drilled effort bounced clear off the Crystal Palace wall.
Ten minutes later and Eddie Howe's men had another shout, this time in the penalty area. Ritchie's cross from the left looked destined for Afobe who was lurking inside the box, but Pape Souare blocked the Scotland international's cross, with referee Mike Jones quickly waving away any claims that it was the defender's hand that did so.
It was, however, the hosts that took the lead on the 27th minute. A smart backheel from Chung-yong Lee gave Wilfried Zaha space on the left and the former Manchester United man crossed for Dann to rifle past Artur Boruc from close range.
Having gone behind the Cherries then responded immediately, and Pugh soon levelled with a fine individual effort. The 28-year-old picked up the ball on the edge of the host's penalty area and chopped his way past his marker before driving an effort passed Wayne Hennessey and into the bottom corner.
Despite a deep cross then finding Souare inside the Cherries penalty just moments later, the Senegalese defender was unable to keep his shot down and the scores remained level going into the break.
The Eagles used the break to make the first change of the evening, as Jordon Mutch replaced McArthur.
A slow start to the second half saw few chances for either side, but it was AFC Bournemouth that eventually created the first and took the lead. Ritchie struck low and had his shot parried by Hennessey, but only as far as Afobe who adjusted well to head the Cherries ahead.
At 2-1 down Palace then made their next move of the evening: replacing Fraizer Campbell with new signing Emmanuel Adebayor. Before Marouane Chamakh was then introduced for Lee.
Having lost their lead, the home supporters became restless and that atmosphere soon infiltrated the on-field action. Adam Smith and Zaha clashed before Steve Cook was booked for a foul on Jason Puncheon.
Eddie Howe then replaced goalscorer Afobe with fellow frontman Joshua King.
With ten minutes remaining, Crystal Palace were still showing signs of levelling. A Ritchie corner was headed clear and the Eagles countered quickly through Chamakh, but Smith felled the substitute and picked up a booking in doing so. Before the hosts struck the resulting set-piece into the stand.
Chamakh soon had another chance to level. Breaking down the left the ball was cut back to the former Arsenal frontman, but his shot from close quarters was parried by Boruc and then cleared by the Cherries defence.
Lewis Grabban was then introduced for the closing minutes, with Ritchie making way.
Substitute Adebayor had a chance to steal a share of the points for the hosts in the dying minutes, but his shot at the back post fell wide of Boruc's post and into the side netting.
Cherries: Boruc, Francis (c), Cook, Gosling, Surman, Pugh, Arter (Distin, 90), Daniels, Smith, Afobe (King, 74), Ritchie (Grabban, 83)
Unused subs: Federici, Iturbe, Murray, O'Kane
Crystal Palace: Hennessey, Ward, Dann, Campbell (Adebayor, 58), Zaha, Lee (Chamakh, 68), Jedinak (c), McArthur (Mutch, 45), Souare, Delaney, Puncheon
Unused subs: Speroni, Hangeland, Kelly, Boateng
Attendance: 24,855 (2,832 away supporters)
Referee: Mike Jones
Yellow cards: Zaha, Cook, Smith, Grabban
Goals: Dann (27), Pugh (33), Afobe (57)