Oveido strike stuns United
Bryan Oviedo piled the pressure on David Moyes by slamming home an 85th-minute winner to end Everton's 21-year Old Trafford hoodoo.
Not since 1992 had the Toffees beaten Manchester United away from home.
For 11 of those years, Moyes had been the man trying.
Here, with Sir Alex Ferguson watching on, Moyes' Everton successor Roberto Martinez managed it at the first attempt.
Oviedo, signed by Moyes last year, arrived with perfect timing at the far post to condemn United to their fourth defeat of the season, which leaves them 12 points adrift of leaders Arsenal and five off the Champions League places.
And United could not say Everton did not deserve their success, for the visitors played with a confidence and verve their hosts could not match.
Wayne Rooney struck a post and came close to netting a rebound before half-time. Former United keeper Tim Howard did brilliantly to repel a Patrice Evra header before Danny Welbeck headed the rebound against the bar after it.
But this Red Devils outfit are a shadow of their former selves and chants of "sacked in the morning" from the gleeful Evertonians, who had waited 21 long years for this success, merely twisted the knife still further.
It turned out Moyes was wrong when he predicted a mixed reception from the visiting fans. Instead it was almost totally negative.
The Scot was booed when he first appeared in his technical area and was then sung a very short and abusive ditty, which confirmed 11 years' service - when he restored Everton's status as a top-half of the table team - counted for little compared to leaving Goodison Park, then returning for coaching staff and two players.
As it happened, only one made the switch and with Phil Jones and Michael Carrick missing through injury, Marouane Fellaini returned to face his former club, still looking to score his first goal for the current one.
If Moyes' transition period has been difficult, Martinez has slotted into the Goodison hot-seat.
Saturday's 4-0 win over Stoke took them above their hosts in the table and they started with the confidence of a team that has lost just once this season.
Lukaku was a menace, with even Nemanja Vidic finding his strength difficult to contain.
The Belgian threatened the home goal at regular intervals, bringing one excellent save out of David de Gea after Vidic had been outmanoeuvred on the United left.
De Gea also denied Kevin Mirallas and with Ross Barkley and James McCarthy also looking to profit from Lukaku's industry, at no stage were United comfortable.
It took them a good 15 minutes to exert any pressure, although after that they seemed to find space easy to come by without really doing much to exploit it.
Evra fizzed a cross into the six-yard area and Ovideo made a vital last-ditch tackle on Antonio Valencia.
Unsurprisingly though, United most dangerous moments centred around Rooney.
The shot that cannoned back off a post had flicked off Phil Jagielka and Sylvain Distin before it reached its destination, and Howard did well to boot the rebound to safety before Shinji Kagawa could pounce.
His failure to turn home Kagawa's low cross shortly afterwards was a shock, even though it flew through a crowd of bodies, if only because of the form he has been in.
Given a second chance, his instinct was right as he hooked the ball goalwards but the power was missing and Everton managed to clear.
United began the second half with Evra launching a powerful drive goalwards.
However, with Everton again taking charge, the natives were getting restless and saw the introduction of Nani and Adnan Januzaj after less than an hour.
The move, which saw Valencia pushed into the right-back slot as Rafael and Kagawa made way, emphasised a lack of invention from United, although Nani blazing over not long afterwards was not exactly the intended response.
In contrast, Gerard Deulofeu almost made an immediate impact after replacing Barkley but again De Gea stood firm.
The flurry of activity that followed at the other end represented United's best opportunity of the contest.
But once Evra, Welbeck and Rooney had failed, the stage was set and Oviedo ensured Everton got the perfect finale.
To rub salt into the wounds, Rooney's booking after 61 minutes was his fifth of the season and he will now sit out the weekend clash with Newcastle.