Back in the team after a hamstring injury, Wilson gave Newcastle the lead in the 88th minute at Selhurst Park by running onto a pass from strike partner Joelinton and sliding a finish through the legs of goalkeeper Vicente Guaita.
Joelinton then broke clear in the 90th, cut onto his left foot and sent in a shot that deflected in off sliding Palace centre-back Gary Cahill.
Newcastle came into the match having lost two straight games, and the win took Steve Bruce's team to 10th place.
The absence of Wilfried Zaha again proved telling for Palace, with Roy Hodgson’s star man also missing in the 1-0 loss at Burnley on Monday after contracting coronavirus.
Palace dropped to 13th, a point below Newcastle.
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Additional reporting by AP.