Wilson poked home an opener against a Toffees side who had started well, but Joelinton's header after the break gave Eddie Howe's men a two-goal lead which they didn't look in danger of surrendering under the lights at Goodison Park.
And they added further gloss to the scoreline when Wilson struck a beauty soon after, with Dwight McNeil grabbing a consolation direct from a corner.
But Newcastle made it four late on when Alexander Isak's sensational run was finished off by Jacob Murphy, who turned in from close range to notch his side's tenth goal in five days - and it could have been even better for the Magpies, had Fabian Schär's late effort from distance not been disallowed after a VAR check.
The hosts made much the better start, with Alex Iwobi fizzing around the final third. One of the Nigerian's crosses narrowly missed the head of Dominic Calvert-Lewin, who was a mobile threat up front in the early stages. Idrissa Gueye twice had a go, with a free kick clearing Nick Pope's crossbar, while McNeil drove straight at Pope from distance as United toiled.
But they gradually grew into the contest, and just before the half hour mark Howe's men moved in front. It still came slightly against the run of play but it was a clinical effort. Matt Targett, in for his first start since September, played in Joelinton down the left, and the Brazilian cut in and took aim. Jordan Pickford parried his strike, but only as far as Wilson, who prodded the loose ball high into the net.
On the stroke of half time, the Toffees thought they had a leveller. McNeil released Calvert-Lewin through the middle and the frontman dinked his finish over Pope with aplomb - but, after a protracted VAR check, their joy was short-lived as the goal was chalked off, with Calvert-Lewin adjudged to have just strayed beyond United's last man, Sven Botman.
Straight after the restart, Joe Willock almost made it two, twisting and turning in the box before seeing his effort blocked on its way to go. Everton remained lively at that stage though, with Iwobi feeding Calvert-Lewin and the hosts' number nine seeing his low strike palmed away by Pope.
Willock nearly grabbed a second with 20 minutes left, and it would have been a special one; his volley from the edge of the box was arrowing towards the corner before Pickford threw a hand at it to divert it past the upright. But two minutes later, the Magpies man did help his side get a second, but it was him who created it - Willock's surging run took him past Ben Godfrey and his centre from the byline was met by Joelinton, who planted his header down into the ground and into the corner.
And by the time Wilson had produced the goal of the night with quarter of an hour remaining, the game was finished as a contest. Bruno Guimarães drove forward from midfield and picked out United's centre forward, who had led the line well all night. He took one touch to get the ball out of his feet before curling a magnificent shot beyond Pickford's reach and into the top right-hand corner.
Though Everton registered a consolation when McNeil's corner somehow crept in at the far post, the Magpies responded immediately and with no shortage of style. Two substitutes combined to hand the visitors a fourth but in truth this owed much to Isak, whose sensational run took him past James Tarkowski, Michael Keane and Ben Godfrey before clipping the ball across the face of goal, where Murphy was there to slam home to slam home Newcastle's tenth goal of a memorable week so far.
It could have been even more of a thrashing by the end. Centre back Schär curled a superb 25-yarder into the bottom corner which looked like it would be number five, but he was denied by a VAR check, with Dan Burn having been offside earlier in the move. Murphy also blazed one over the top in stoppage time, meaning that Howe's men had to settle for four goals at the end of another terrific evening for United's travelling supporters.
