Javier Hernandez headed home an 84th-minute winner to send Manchester United to the brink of a record 19th league title.
The Mexican had come closer than any other United player to breaking the stubborn resistance of an Everton side who could have had a couple of penalties and for whom goalkeeper Tim Howard was outstanding.
But additional heroic performances from Phil Jagielka and Sylvain Distin counted for nothing as Hernandez rose to meet Antonio Valencia's far-post cross.
The striker powered in his 19th goal of a sensational debut campaign to send United into the Champions League semi-final with Schalke in winning mood and knowing if they can avoid defeat to Arsenal and Chelsea in their next two league games, they will surely knock Liverpool off the perch they have occupied for so long.
Faced with a familiar selection poser, knowing the following four games, starting with the first leg of that Champions League semi-final against Schalke in Gelsenkirchen on Tuesday, would shape his side's season, Sir Alex Ferguson came up with a typical mixture of solid and experimental.
Jonny Evans was fortunate referee Peter Walton did not view his tackle on Jermaine Beckford as a foul midway through the opening period and Darron Gibson's normally reliable long-range shooting was way off beam.
However, back in the dug-out after completing his five-match touchline ban, Ferguson could be reasonably pleased with his side's first-half efforts, save for the fact they did not actually score.
The time when picking Hernandez was viewed as a gamble has long since passed and predictably, the fast-moving Mexican was the hosts' biggest threat.
In Howard though, Hernandez was faced with a goalkeeper who has special reason to do well at this venue given he enjoyed three seasons with the Red Devils until joining the Goodison Park outfit, initially on loan, in 2006.
Ferguson's concern about the American had more to do with his concentration levels than any problems with ability.
And Howard proved his worth after 25 minutes when Hernandez was sent sprinting through by Anderson's slide-rule pass and let fly from an acute angle.
Howard plunged to his right to make an excellent save by his near post.
The American's next effort was even better as he beat away another Hernandez effort after the striker had been set up by Valencia and Wayne Rooney.
Hernandez then did Howard's job for him eight minutes from half-time.
Valencia's superior strength allowed him to shove Leighton Baines off the ball and roll a pass back to Nani, who had already wasted one early opportunity by taking too long to decide what to do.
This time, Nani went for goal straight away. He would surely have found it too had the ball not struck Hernandez, who had slipped as he made his way in the penalty area, and deflected harmlessly away.
There could barely be any discussion about who was on top.
Everton manager David Moyes could take pride in his team's battling qualities, which were exemplified by the stoic defending of Jagielka and Distin, who managed to get in the way of an Hernandez cross that was about to give Fabio a tap-in.
Moyes had even more reason to admire the manner his side started the second period as United failed to rouse themselves.
The introduction of Tim Cahill helped and how Rio Ferdinand got away with shoving second substitute Victor Anichebe over when the Everton man had outpaced him in a race towards the United goal was difficult to fathom.
Everton's luck was also out midway through the half when Jack Rodwell let fly from the edge of the area with a shot that took a deflection off Evans and was heading for the bottom corner until Edwin van der Sar got the slightest touch.
The fluidity had disappeared from United's play, so they dug into their reserves of self-belief.
Distin turned a Fabio cross onto his own post before the introduction of Ryan Giggs, then Anderson got no power at all into a 10-yard shot after being offered a decent sight of goal.
The hosts' momentum gathered pace. Rooney's free-kick tipped over by Howard. Valencia's thunderbolt cannoning into Jagielka. Another brilliant Howard save to deny Hernandez.
Could Everton hold out when so many others had failed? Hernandez ensured the answer was rather predictable.Reuse content