Both sides came into the game on the back of disappointing defeats as Everton lost 2-0 at relegated Fulham last weekend, while United crashed out of the Champions League at Barcelona in midweek.
The Red Devils have won more games against Everton than any other team in the Premier League, but their quest to make it 37 started badly when Richarlison spectacularly put the Toffees in front after 13 minutes.
Gylfi Sigurdsson piled more misery on United with a pile-driver of a strike just before the half-hour mark, before second half goals from Lucas Digne and Theo Walcott completed the rout.
United’s fifth successive defeat in all competitions for the first time since 1981 leaves them in sixth position – two points behind Arsenal in fourth – while the Toffees move up to seventh place.
Everton made two changes to the side that lost at Fulham last time out as Michael Keane and Morgan Schneiderlin replaced Phil Jagielka and the suspended Andre Gomes.
Ashley Young, Scott McTominay and Jesse Lingard were replaced by Diogo Dalot, Nemanja Matic and Romelu Lukaku in three changes for Manchester United.
Everton started strongly and almost went ahead in the 11th minute when the ball dropped kindly to Richarlison in the United area, but David De Gea produced a fine reaction save to deny him and the Brazilian’s follow-up effort went wide.
United failed to take heed of that warning as the hosts did go in front just two minutes later when Dominic Calvert-Lewin flicked on Digne’s long throw-in and the ball dropped to Richarlison who produced an acrobatic overhead kick to beat De Gea from eight yards.
Everton continued to dominate, while United’s first effort of note came on 19 minutes when Marcus Rashford got in down the left of the area but lifted a right-foot effort over the goal when aiming for the far corner.
It was 2-0 in the 28th minute when Sigurdsson picked up possession in the middle of the United half and was allowed to advance before smashing a fierce 25-yard right-foot strike past beyond the dive of De Gea.
The tempo of the game dropped following the second goal as United showed no signs of reducing the deficit ahead of the half-time interval.
It was more of the same after the break and, despite losing Richarlison to injury, Everton managed to extend their lead on 56 minutes.
A corner played in from the left was cleared by a combination of De Gea and Chris Smalling to Digne, who was just outside the area, and he thumped a superb first-time left-foot strike back into the bottom corner.
The situation became embarrassing for the visitors on 64 minutes when Sigurdsson sent Walcott clear down the left channel and he raced into the box to slot Everton’s fourth of the game past De Gea.
Seamus Coleman looked to get in on the act on 81 minutes with a left-foot strike from the right edge of the area, but De Gea got down well to gather.
Anthony Martial had United’s first attempt on target in the 86th minute when he was teed up by Paul Pogba, but Jordan Pickford made a fairly comfortable save.