Scott Dann put Palace in front a minute after halftime after Damien Delaney had flicked on Jason Puncheon’s cross.
After withstanding intense second-half pressure from Bournemouth, Christian Benteke made sure of all three points when he headed in a cross from substitute Andros Townsend.
Palace, who gave a debut to wing back to Patrick van Aanholt, signed on Monday from relegation rivals Sunderland, had gone closest in an uninspiring first half.
(Reporting by Neville Dalton; Editing by Toby Davis)
0 votes