The Eagles put three past the league's best defence, with Hayley Ladd, Kirsty Howat, and Abbie Larkin all scoring at Selhurst Park.
Palace went behind to a first-half Amalie Thestrup goal before Ladd levelled things with a stunner from outside the box.
Howat put Palace ahead just after the break, before Larkin made it three with a powerful header.
Emma Bissell's penalty made it a nervy final few minutes, but Palace held on to secure a massive three points in SE25.
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