Gylfi Sigurdsson scored Everton's second goal with a fierce strike from outside the area
Everton produced a thrilling display to outclass a woeful Manchester United at Goodison Park and expose all the problems facing Red Devils manager Ole Gunnar Solskjaer.
United face a fight to secure a Premier League top-four place and Champions League football next season after 90 minutes which were little other than torture against a rampant Everton.
United goalkeeper David de Gea had saved superbly from Richarlison before the Brazilian hooked in an acrobatic 13th-minute volley to set the tone for a magnificent display from Marco Silva's side.
De Gea was beaten by Gylfi Sigurdsson's low 25-yard drive, going down late, as Everton took total control.
Everton did not let up after the break, Lucas Digne scoring from long range after De Gea punched out a corner, before substitute Theo Walcott ran clear on to Sigurdsson's pass to slide home the fourth.
United have lost six of their past eight games in all competitions, while a fifth successive away defeat - for the first time since 1981 - leaves them facing the prospect of Europa League football next season.
Everton in devastating form
Everton are on a hot streak at Goodison Park but this can rank alongside the finest displays seen at the famous old stadium in many seasons.
Yes, much will be made of United's obvious deficiencies, but it would be a gross injustice to ignore a magnificent performance from a side who have drawn with Liverpool and beaten Chelsea, Arsenal and United in their past four home games without conceding a goal.
Everton swarmed all over United from the first whistle and there was never a moment when they looked like relinquishing control.
Silva's pressing approach saw United harassed mercilessly for 90 minutes, but this was not simply about work-rate - Everton were full of skill, pace and athleticism.
Idrissa Gueye was the fulcrum in midfield while Sigurdsson and the gifted Brazilian Bernard were the creators-in-chief from first to last.
There may have been some doubts expressed about Silva's position not so long ago, but this blistering run of home form - and a style which will win full favour from Everton's fans - surely means he will be given time to build, as he should.
Man Utd a heartless, abject shambles
United were reduced to being ironically cheered by their own supporters for merely stringing three passes together with Everton 4-0 up and in cruise control.
And, yes, it was that bad.
Solskjaer's side were quite simply over-run and did not even show the heart or fighting spirit to escape from a joyous Goodison with any dignity on a desperate day.
There was simply nothing good about this United performance. Indeed, given Everton's superiority, they were fortunate the scoreline did not have an even more embarrassing appearance.
Paul Pogba strolled around midfield while Gueye, Morgan Schneiderlin and Sigurdsson snapped into challenges, and it was a nightmare return to Everton for striker Romelu Lukaku.
Taunted throughout, he could not do a thing right and his afternoon simply went from bad to worse.
He was not alone. De Gea may have saved well from Richarlison early on but he was slow to react to Sigurdsson's shot and it was his punch that fell at Digne's feet to score. The Spain keeper is having a mixed season.
It was five years ago to the day since a 2-0 loss here ended David Moyes' reign - and this United performance was even worse than that.
Solksjaer has inherited a mess, the early gloss from his arrival has worn off and players like Pogba and Lukaku, who were revived after Jose Mourinho was sacked, look back to their bad old ways.
Now there is the small matter of the derby against title-chasing Manchester City at Old Trafford on Wednesday.
Man of the match - Gylfi Sigurdsson (Everton)Gylfi Sigurdsson scored one goal and assisted another'I want to apologise' - what they said
Everton boss Marco Silva, speaking to Sky Sports: "I'm delighted with the players. It's important to remind you what we did in the last four home games - we're on a fantastic run.
"Our last performance away was not good enough and we must show something different. We did. We were the best team on the pitch from the first to last minute.
"When we won against Chelsea we were 26 games without a win against the top six. After we won I said we will change that, and now we are playing with quality at home.
"It's important to see our fans enjoying what we are doing - everything what I want as a manager. We are doing really well. Last seven games, five clean sheets."
'Nowhere near good enough' - Solskjaer apologises to Man Utd fans
Man Utd manager Ole Gunnar Solskjaer, speaking to BBC Sport: "We were beaten on all aspects today. The only place we beat Everton - I can't say we beat them - but we had a fantastic support and I just want to apologise for the performance we turned out.
"We have been fantastic for long periods and it's a tough league to get into the top four, never mind winning the league. There are six teams there and Everton want to be in there.
"We know it's a big task and work to be done. We have to do it together; we have to get on with it because this is not good enough.
"You have got to start somewhere and we will give it everything we have got with the last four games - massive games with City and Chelsea coming to Old Trafford. That's where we get the best support in the world.
"We can turn it around. In football, like in life, things can change quickly. We have got to change it from bad to good.
"We need a game of football as soon as we can as we need to get this out of the systems.
"Everyone here can say with hands on hearts that's not good enough - not worthy of a Manchester United team. We know that and apologise again to fans."
Man Utd continue to struggle on the road - the stats
This was Everton's biggest margin of victory over Manchester United in any competition since beating them 5-0 in October 1984.It was United biggest defeat to any opposition since a 4-0 loss to Chelsea in October 2016.This was United's fifth consecutive away defeat in all competitions, their longest such run of losses since March 1981 under Dave Sexton (also five).United have conceded 48 Premier League goals in 2018-19, their highest tally in a single season in the competition and their most in a league campaign since 1978-79 (63).Everton have won more points at home to the 'big six' clubs this season (10 - P6 W3 D1 L2) than any other team outside the top six.United have gone 11 consecutive matches without a clean sheet in all competitions for the first time since 1998.Everton have now won four of their past seven home league games against United (D1 L2); they had won only three of their first 20 Premier League games against them at Goodison Park before this (D3 L14).Only Andrei Kanchelskis (15 in 1995-96), Yakubu (15 in 2007-08) and Romelu Lukaku (15 in 2013-14) scored more Premier League goals in their debut season with Everton than Richarlison this term (13).Gylfi Sigurdsson has been directly involved in nine Premier League goals against Manchester United (five goals, four assists), more than he has against any other club.United goalkeeper David de Gea has conceded eight goals from outside the box in the league this season, the only campaign in which he has conceded more was 2013-14 (9).What's next?
Manchester United host Manchester City in the derby on Wednesday at 20:00 BST, and Everton visit Crystal Palace on Saturday at 15:00.