Luka Milivojevic curled a free kick over the wall and into the top corner from 25 yards (meters) in the 12th minute, before Jordan Ayew finished off a flowing move involving Wilfried Zaha and Patrick van Aanholt in the 23rd.
Palace has now gone a club record of four Premier League games without conceding a goal. While Palace moved up to ninth place, and just four points off fifth-place Manchester United in what is currently the final Champions League qualification spot, Bournemouth is in a relegation fight as it looks to secure top-flight soccer for a sixth season.
Bournemouth is third from last on 27 points, behind West Ham on goal difference.
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