Just five days on from crashing out of the UEFA Champions League quarter-finals at the hands of Barcelona, Ole Gunnar Solskjaer's side produced a dismal performance to slump to another heavy defeat.
Well-taken goals from Richarlison and Gylfi Sigurdsson had the Toffees 2-0 up at the break before Lucas Digne's sweetly struck effort and Theo Walcott's cool finish completed a memorable win.
United is two points off fourth, and thankful that Arsenal failed to overcome Crystal Palace, and the inquest will surely soon begin after a nightmare outing that strikes a huge blow to its hopes of featuring at Europe's top table next season.
Richarlison had already brought a fine reaction stop from David De Gea on the bounce by the time he opened the scoring.
Dominic Calvert-Lewin flicked on Lucas Digne's header and the Brazil forward lashed home an unstoppable acrobatic volley.
Marcus Rashford flicked over the top from Paul Pogba's long punt but United's situation worsened after 28 minutes.
Everton broke from a United corner, leading to Sigurdsson cutting inside from the left and drilling low into the near corner from 25 yards.
The game was all but done 10 minutes after the break when Digne showed sensational technique on the half-volley to leave De Gea no chance.
Further humiliation was to follow and Sigurdsson carved United open again to play through substitute Walcott, who slotted past De Gea one-on-one to cap off a day to forget for Solskjaer and his team.