Bournemouth’s £10million signing from Wolves netted from a second-half header to aid his side's fight against relegation and condemn Palace to a fifth straight Premier League defeat.
Palace had taken the lead in the first half when Scott Dann converted Wilfried Zaha's cross but Bournemouth equalised seven minutes later through Marc Pugh.
Afobe's winner in the 57th minute put paid to Emmanuel Adebayor's hopes of a dream Palace debut – the Togolese striker had scored in all of his previous Premier League debuts but this time it was not to be.
The defeat leaves Palace stuck on 31 points and in the middle of their worst run under Alan Pardew, while Bournemouth's hopes of staying in the division are being strengthened by their continued success away from home.
In a lively start, Zaha set Joel Ward free on an attack inside the first minute of the game, and his low cross forced Andrew Surman into a last-ditch clearance to prevent an early goal for Palace.
Bournemouth should have taken the lead when Charlie Daniels picked out Afobe with a cross that found the striker unmarked, but he badly mistimed his shot and failed to trouble Palace goalkeeper Wayne Hennessey.
The breakthrough for Palace came courtesy of a brilliant back-heeled pass from Lee Chung-yong, who created the space for Zaha to fire a low cross that Dann smashed high into the net with a side-footed volley.
The goal was the first in the Premier League by a Crystal Palace player since mid December and the relief around Selhurst Park was palpable, but the lead was short-lived.
Bournemouth surged forward and Matt Ritchie played in Pugh, who turned Dann twice on the edge of the box before hooking a shot into the bottom-right corner of the net.
Palace burst out of the blocks after half-time, and both Fraizer Campbell and Jason Puncheon spurned good chances, but it was Bournemouth who turned the game just before the hour-mark.
Hennessey made a brilliant save from Ritchie's powerful shot from the edge of the box but Afobe was quick to react and head home the rebound.
Pardew responded by introducing Adebayor and Marouane Chamakh to try and turn the game, but Bournemouth frustrated their hosts and Zaha in particular struggled to keep his cool as chances went begging.
Adebayor was restricted to half chances as he chased a debut goal, and the groans that echoed around Selhurst Park as Mile Jedinak's free-kick sailed over his head in the dying minutes summed up a frustrating outing for Palace. Key Opta stats: - Benik Afobe scored his third goal in four games since joining Bournemouth and scored in three consecutive games for the first time since April 2015. - After losing five of their first six away Premier League games, Bournemouth have lost just one of their last seven (W3 D3 L1). - Seven of Palace's 25 goals this season have come from defenders, a Premier League high.