It looked as if the Premier League clash was heading towards a stalemate before Wilson's seventh goal of the season in the dying stages broke the deadlock before Joelinton's deflected finish doubled Newcastle's lead 100 seconds later to seal the victory in South London.
Karl Darlow continued his positive form in between the sticks with a string of strong stops as the Magpies also recorded their second league clean sheet of the season, their first since a 2-0 win against West Ham United on the opening day of the 2020/21 campaign, as Steve Bruce's side leapfrogged Roy Hodgson's Eagles into the top half of the table.
The visitors began brightly in the opening minutes of the contest as Miguel Almirón played a neat pass into Joelinton's path before the Brazilian's low cross into the six-yard area almost found Wilson but the ball was crucially cleared by the sliding Gary Cahill.
Darlow was forced into action before the hour-mark after beating away Eberechi Eze's fizzing strike from outside the penalty area, with the 30-year-old shot-stopper equal to the swerving ball.
The United goalkeeper was alert minutes later to turn away Jeffrey Schlupp's stringing drive towards goal after the Palace forward drove dangerously into the box but his powerful strike towards the near-post was blocked by Darlow's strong right hand.
Joelinton almost punished a weak pass from Eagles skipper Scott Dann on the edge of the box but the forward's low effort towards goal lacked the power to trouble Guaita and the effort was comfortably held by the diving Spaniard.
In the second half, Palace went close to breaking the deadlock as the ball broke kindly for Jordan Ayew inside the penalty area following Schlupp's tricky run but the Ghanaian could only poke his effort wide of the target, with right-back Javier Manquillo doing enough to put the forward off.
Wilson almost gave the visitors the lead shortly after the hour mark as the striker rose high to meet Manquillo's bending cross from the right wing but the striker, returning from a hamstring injury, steered his header narrowly wide of the left-hand post.
Matt Ritchie made his first appearance since sustaining an acromioclavicular joint injury at Tottenham Hotspur in September after replacing Almirón and went close to making an instant impact from the substitutes' bench in the latter stages but his fiercely driven free-kick was directed straight at Guaita.
Palace substitute Christian Benteke leapt from Patrick van Aanholt's cross but saw his towering header kept out by the alert Darlow, who got down quickly to turn the ball away to safety.
Federico Fernández then produced a crucial block to deny Cheikhou Kouyaté from getting a shot away at goal from inside the penalty area as the Argentine centre-back threw himself bravely at the midfielder's ferocious half-volley.
The hosts wasted a huge opportunity to open the scoring shortly after as the ball found its way to Van Aanholt on the left but the former Newcastle left-back fired the ball across goal, narrowly evading the incoming Michy Batshauyi.
With the full-time whistle beckoning, United looked to have snatched an important victory as Wilson broke the deadlock in the 88th minute.
After combining brilliantly with Joelinton, Wilson eventually got onto the end of of a fine through pass from the Brazilian before cooly tucking the ball home from close-range through the legs of Guaita.
There was still time left for United to double their lead barely two minutes later as Joelinton, a workforce all evening, netted his first league goal of the season after racing onto Wilson's pass before cutting inside and firing a low effort beyond Guaita to confirm a first top-flight away win at Palace since 2013.
Newcastle United: Karl Darlow, Javier Manquillo, Federico Fernández, Ciaran Clark, Jamal Lewis, Jonjo Shelvey (c), Sean Longstaff, Jeff Hendrick, Miguel Almirón (Matt Ritchie 68), Joelinton (Fabian Schär 90), Callum Wilson.
Subs not used: Mark Gillespie, DeAndre Yedlin, Matty Longstaff, Jacob Murphy, Elliot Anderson.
