The striker has impressed since his arrival on loan from Chelsea, netting six in 13 appearances for a team that had previously struggled for goals.
Batshuayi will now return to Stamford Bridge unless Palace can find what is likely to be a club-record transfer fee to retain him.
— Crystal Palace F.C. (@CPFC) May 12, 2019
Palace lost the similarly influential Ruben Loftus-Cheek in near-identical circumstances a year ago and are still to convincingly replace him, despite a final-day win to conclude a more impressive season in which they have finished an encouraging 12th.
Defeat represented Bournemouth's eighth from their last 14 games, and a continuation of the struggles that began in November which, if not arrested, will quickly leave them threatened by relegation when the next Premier League season begins.
Eddie Howe's team slid to 14th after being overtaken by Newcastle – 4-0 winners at Fulham – and were largely flattered by their three goals.
Palace's cause was hindered by Scott Dann failing a late fitness test, forcing Roy Hodgson to partner Joel Ward with Martin Kelly in the centre of an unfamiliar back four.
Regardless, they were the stronger team as they played with intensity, and threatened to win by a wider margin after Batshuayi's 24th-minute strike gave them the lead.
The superb Wilfried Zaha's cross from the right wing deflected high into the air off Adam Smith, with Batshuayi taking advantage of Bournemouth's static defence to swivel in the six-yard box and volley in with conviction.
His second followed eight minutes later, when Zaha's through-ball released Aaron Wan-Bissaka into space on the right, from where he sent a low ball across the face of goal that Batshuayi effortlessly sent first time beyond teenage goalkeeper Mark Travers.
Zaha was almost rewarded with the goal he deserved after a further five minutes, with James McArthur's through-ball putting him into space near the half-way line.Zaha then carried possession into the visitors' penalty area from where he had to stretch to shoot, leaving Travers with a simple save that rebounded off Jack Simpson and rolled in.
Jefferson Lerma unexpectedly struck for Bournemouth on the stroke of half-time, when Nathaniel Clyne found him in midfield, allowing him to run into space and fire home into the top-left corner.
The Cherries were given hope of a comeback 12 minutes into the second half when a cut-back from the left from Smith found Jordon Ibe on the edge of the area, with his low, goal-bound shot deflecting off Ward and beyond the unfortunate Vicente Guaita's reach.
Goals from Lerma, Ibe and King not enough at Selhurst Park.
The match report from topsy-turvy #CRYBOU.
— AFC Bournemouth (@afcbournemouth) May 12, 2019
Zaha was again crucial in the goal that effectively ensured a home victory. After receiving possession from Patrick van Aanholt, he took out three defenders by turning and playing the return pass that left the Dutchman to routinely finish from close range.
Joshua King's 73rd-minute, back-post strike, after Chis Mepham had flicked on Ryan Fraser's corner, again narrowed the visitors' deficit, before Andros Townsend added Palace's fifth seven minutes later.
Zaha, again, ran from inside his own half, beat two defenders, reached the penalty area and fed Townsend to his right, who struck first time into the far, left corner.