Leon Osman's swerving 32nd-minute shot put Everton in front at a raucous Goodison Park and, although the home side were reduced to 10 men when Steven Pienaar was red-carded for a rash tackle after 61 minutes, City could not reply.
Substitute Nikica Jelavic sealed victory deep in stoppage time after being set up by a rampaging Marouane Fellaini.
United needed no second invitation to open a 15-point lead in the title race although only Wayne Rooney's deflected early shot separated them and second-bottom Reading at Old Trafford.
Sir Alex Ferguson's side never required top gear as they rolled on towards a 20th English title with their 24th victory in 29 league games this season, although the Scot refused to accept that the race was won.
"We have got Sunderland away in our next game, which is always a tough place to go, and then we face Manchester City at home," he told ESPN.
"You don't get points and medals for being complacent," added Ferguson whose side have 74 points ahead of City on 59.
Everton briefly rose above Arsenal into fifth spot with 48 points in the battle for a top-four position but the Gunners responded with a 2-0 victory at Swansea City.
Boosted by a surprise, if ultimately fruitless, Champions League win in their last 16, second leg tie at Bayern Munich on Wednesday, Arsenal struck late through Nacho Monreal and Gervinho.
"It was a difficult game away to Bayern in midweek. The spirit we showed today was fantastic. We're up for the battle," Wenger told Sky Sports.
Liverpool lost 3-1 at Southampton to virtually extinguish their top-four hopes and hand Saints a major boost in their bid to steer clear of trouble at the bottom of the table.
In a thrilling relegation scrap, Aston Villa clawed their way to a vital 3-2 victory over bottom club Queens Park Rangers.
Christian Benteke scored the winner after 81 minutes to leave QPR seven points adrift of the safety zone.
QPR, seeking a third consecutive league win, led 1-0 thaansk to Jermaine Jenas and then equalised through Andros Townsend having gone 2-1 behind before Benteke grabbed his 13th league goal of the season.
Everton, one week after being booed and heckled by their fans in an embarrassing 3-0 FA Cup quarter-final defeat at home to struggling Wigan Athletic, produced a gutsy performance to remain in contention for a top-four finish.
"Last week was disappointing but we showed when we are at the races we are a match for any team," said Osman, who is in England's squad for this month's World Cup qualifiers against San Marino and Montenegro.
His strike was a special one, the midfielder having received the ball from Seamus Coleman 25 metres out before lashing a shot past helpless England keeper Joe Hart.
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