Jamaal Lascelles' own goal had given the hosts a first half lead under the lights, but the Magpies' skipper atoned just a minute later as his header struck the crossbar and was inadvertently turned in by Mason Holgate to hand Eddie Howe's men an equaliser.
It was a pulsating encounter but after the break, United shifted through the gears as Fraser's first goal of the campaign and Trippier's superb free kick clinched the points for United, who recorded back-to-back Premier League wins for the first time in 2021/22.
A breakneck first half took little time to fire up. Jonjo Shelvey intercepted a wayward pass from Yerry Mina before blasting just over, and it was the United midfielder who forced the first save of the night, shooting straight at Jordan Pickford under pressure from Anthony Gordon.
The quick pace of the game reflected both Newcastle's freshness after 16 days without a competitive game and Everton's early rejuvenation under new manager Frank Lampard, who oversaw a 4-1 FA Cup win over Brentford during his first game in charge at the weekend.
Richarlison pulled an effort wide and former Magpie Andros Townsend saw a curling strike deflected wide before the Toffees lost both Demarai Gray and, later in the half, Mina to injury, forcing a reshuffle and the introductions of debutant Dele Alli and centre back Jarrad Branthwaite.
But after Richarlison had seen his neat flicked finish chalked off for offside, the visitors struck. Gordon's free kick into the box took a fortunate touch which allowed Alli time to shoot, and though his attempt was blocked, the rebound cannoned in off a helpless Lascelles just a couple of yards from goal.
The Newcastle captain redeemed himself just a minute later, however. Trippier's set piece deliveries had caused a few problems for Lampard's side and it was his corner that was met by Lascelles, whose thumping header struck the crossbar. This time it was Howe’s men who benefitted from a fortunate rebound, with the ball striking Holgate on its way into the net.
United finished the half strongly, with Fraser's header blocked by Branthwaite, but Gordon called Martin Dúbravka into action after the restart as the contest continued to entertain. It was a fiesty affair by that stage – Shelvey's first half tackle on Gordon, for which he was booked, had set the tone, while Allan Saint-Maximin came in for a couple of knocks at the hands of the Toffees.
Ten minutes into the second period, though, United stole in front. Possession was well kept by Chris Wood and Joelinton, allowing Saint-Maximin to cross from the byline. It took a nick on its way over, flummoxing Pickford, and Fraser was there to turn it in despite the best efforts of Townsend on the goalline.
With quarter of an hour left, Newcastle thought they had extended their lead when a Shelvey pass released Saint-Maximin on the left. The Frenchman cut inside and saw his low shot parried by Pickford and Wood was there to bundle it home, but the offside flag denied him a first goal in black and white.
But barely five minutes later, Howe's charges made sure of the points. From 25 yards, in front of the Gallowgate End, Trippier – outstanding all game – stepped up to take the free kick. His strike swerved around the wall and dropped just inside Pickford's left-hand post, sending the United faithful wild.
It could have been more in the end, too, as substitute Jacob Murphy – sent on alongside debutant Bruno Guimarães – struck the base of the post and both Joe Willock and Saint-Maximin tested Pickford late on, but those Fraser and Trippier goals proved enough to secure a deserved first home win of 2022.
