Gayle put his team ahead after 23 minutes, heading home from close range after Jacob Murphy’s effort had been kept out by Thibaut Courtois.
And Pérez’s brace after the restart ensured United’s four-game winless run came to an end in style, as the hosts dashed Antonio Conte’s side’s hopes of qualifying for the Champions League in the process.
It was a thoroughly dominant display from Rafa Benitez’s Newcastle, who made it another final day to remember following last term’s title-winning victory over Barnsley and the 5-1 drubbing of Tottenham Hotspur in 2016.
The hosts began brightly in the St. James’ Park sun. Jonjo Shelvey stung the palms of Thibaut Courtois, and his central midfield partner Mo Diamé also went close, seeing his vicious shot tipped past the post by the Belgian.
Diamé, dominating once more in the middle, robbed N’Golo Kante before firing just wide as Benítez’s continued to apply pressure, and they were rewarded midway through the half.
Matt Ritchie – with little backlift – picked out Murphy at the back post, and his unusual effort looped over Courtois and looked to be dropping just under the crossbar. The Blues’ stopper reacted brilliantly to claw the ball off the line, but Gayle was waiting, perfectly placed, to nod home the opener.
Seconds later, Shelvey collected a pass on the edge of the area and jinked past Ross Barkley before blasting over, and Gayle’s low drive again tested Courtois. United finished the first period strongly, too, with Pérez dragging an attempt past the upright..
Chelsea, who needed a win to have any chance of finishing in the top four, threatened the Magpies’ goal for the first time after the break. It took 50 minutes, but when Olivier Giroud flicked Barkley’s cross goalwards, Martin Dúbravka pulled off a magnificent stop, backpedalling and stretching to tip it over.
But their hopes of a fightback took another hit just before the hour. A poor clearance from Tiemoue Bakayoko only reached Shelvey, who half-volleyed it goalwards. The shot looked to be on target, but Pérez got the faintest of touches to it to help it on its way into the bottom corner.
It was, in truth, no less than Newcastle deserved. The visitors’ midfield were enduring a torrid afternoon at the hands of Shelvey and Diamé, and on the rare occasions Antonio Conte’s side looked to have found a way through, they found Dúbravka in defiant mood. He saved excellently from Barkley with his legs, just before United’s third.
Ritchie, tireless once again, whipped a free kick to the back post, where Florian Lejeune helped it back across goal. Pérez was there again, well-placed to turn it home in front of the Gallowgate End and put the result beyond doubt.
Chelsea pushed forward in the final ten minutes, with Alvaro Morata, Willian and Pedro all summoned from the bench, but they never really looked like breaking down the Magpies, who closed the campaign in the perfect manner – with three goals, a clean sheet and a convincing victory.