The Eagles were undoubtedly led by talisman and captain Wilfried Zaha, but the entire team put in a shift to secure three points in a confident, dramatic game.
The action started early, with Andros Townsend bagging after seven minutes to hand Palace the advantage. Then, in the second-half, Zaha saw a goal disallowed before Jordan Ayew secured a penalty for Victor Lindelof's handball.
Although David de Gea blocked Ayew's resulting spot kick, he was judged to have done so illegally, and Zaha made no mistake from the retake.
United signing Donny van de Beek then pulled a goal back to tee-up a tense final 10 minutes but Zaha ensured Palace returned with three points by netting his second just minutes after.