Coming off miserable defeats to Chelsea, Tottenham and Atalanta, the Blues needed to put in a performance to show concerned supporters that they are capable of getting their 2017-18 season back on an even keel and there signs of that in a contest that was fairly even following Antonio Valencia's early opener.
Ronald Koeman's men would finish the match having had more possession than their hosts but Everton's now familiar lack of attacking heft precluded a fightback and United capitalised on their fatigue in the closing stages to score three more goals.
Deploying a five-man back line aimed at trying to stifle Jose Mourinho's attack Koeman was no doubt also hoping to stem the tide of goals that had seen his team concede eight goals without reply in those preceding three matches.
The clean sheet lasted just four minutes but there was little Everton could have done to prevent it as Nemanja Matic found Antonio Valencia with a switch ball from left to right and the Ecuadorian lashed a crisp half volley past Jordan Pickford from 25 yards out.
With Tom Davies justifying his selection in midfield, the visitors set about trying to re-establish parity and Wayne Rooney came close to marking his first game back at Old Trafford as an opposition player but dragged a shot from Cuco Martina's square ball wide of the far post.
Romelu Lukaku, himself facing his old club for the first time, should have doubled United's lead following a poor pass by Michael Keane but he fired wide when he looked odds-on to score.
Rooney was denied by David de Gea following a great run by Tom Davies early in the second half, the Spaniard parrying the veteran striker's shot from close range and he foiled Gylfi Sigurdsson from a similar position before Juan Mata rattled a free kick off the post.
With the game still close heading into the final stages and Koeman having made all three of his changes in attempt to find an equaliser, it was a rare slip on the day by Ashley Williams that effectively killed the game.
The Welsh international gifted the ball to Marouane Fellaini in the centre of the park, he fed Lukaku who in turn teed up Henryk Mkhitaryan and he supplied a clinical finish to make it 2-0.
That became 3-0 shortly afterwards when Lukaku poached the goal Evertonians had feared at the far post and wheeled away cupping his ear to the away fans.
Substitute Sandro Ramirez stung De Gea's palms with an excellent drive but a late penalty, scored by Anthony Martial after a somewhat harsh penalty award for handball on Morgan Schneiderlin, capped another depressing day for Everton.
The result leaves the Toffees in the relegation zone for the first time in seven years and increases the pressure on Koeman to find a resolution to his side's awful sequence of results and goalscoring woes, although some heart will be taken from a performance that could only have been an improvement on the debacle in Italy three days ago.