Recovering from conceding the opening goal to Scott Dann, they went seven points clear of the relegation zone after Marc Pugh and Benik Afobe scored either side of half-time.
The result leaves 11th-placed Palace winless in the league since December 19, and further away from finishing in the top six which had once looked a realistic ambition.
Mile Jedinak and James McArthur replaced the injured Yohan Cabaye and Joe Ledley from the team which on Saturday defeated Stoke 1-0 in the FA Cup.
In-form winger Wilfried Zaha, perhaps expectedly, was influential in the opening goal which came in the 27th minute. Collecting possession from Chung-yong Lee’s backheeled pass, he sent a powerful cross towards Dann which the defender impressively volleyed beyond goalkeeper Artur Boruc and into the back of the net.
However, Dann was outclassed in his defensive role for Bournemouth’s equalising goal.
In the 34th minute, Pugh displayed fine footwork to turn the defender and create space from 15 yards, whereupon he then sent a composed finish past Wayne Hennessey and into the bottom-left corner.
Palace manager Alan Pardew had resisted selecting Emmanuel Adebayor against Stoke and, owing to a lack of match fitness, had only named him as a substitute, but after Pape Souare and Zaha missed with reasonable chances towards the end of the first half, the temptation grew early in the second.
The striker was already poised for his debut when another significant January signing, Bournemouth’s £10m Afobe, threatened to ruin it. Matt Ritchie forced a fine save from Hennessey with a close-range shot, and Afobe, sensing a chance to score his third goal in three games, pounced unchallenged from inside the area to head the rebound inside the left post.
Adebayor was introduced for Frazier Campbell immediately afterwards, but he could not rescue a point for Palace.
Hennessey, Ward, Dann, Delaney, Souare, Jedinak, McArthur (Mutch 46), Zaha, Puncheon, Lee (Chamakh 68), Campbell (Adebayor 58).
Boruc, Smith, Francis, Cook, Daniels, Surman, Ritchie (Grabban 85), Gosling, Arter (Distin 90), Pugh, Afobe (King 75).
Mike Jones (Cheshire).