Juan Mata's 87th-minute shot deflected off the inside leg of Phil Jones and found the corner to settle a dull match at Old Trafford that ended with the sending-off of United defender Rafael da Silva for a petulant kick at David Luiz.
Chelsea strengthened its grip on third place and can virtually seal a place in Europe's top competition next season by beating fifth-place Tottenham at home on Wedneday. Arsenal is a point behind Chelsea and Spurs a further two adrift.
"We are in the driving seat now," said Chelsea manager Rafa Benitez, who got the better of longtime counterpart Alex Ferguson as he did in the FA Cup quarterfinals last month. "If we can win (against Tottenham), we can be there (in the Champions League)."
While the race for a top-four finish could yet go down to the wire, Everton's European hopes were virtually ended by only drawing 0-0 at Liverpool in the 220th Merseyside derby at Anfield.
Everton, which hasn't won at Anfield in 14 years, can at least take solace from the fact it is likely to finish above its neighbour for the second straight season — something the blue half of Merseyside hasn't achieved since 1937.
Everton needs one win from its final two games to guarantee being the city's top team but is now five points behind Spurs with two matches left.
The fifth match of the season between old foes United and Chelsea was comfortably the worst, only coming to life in the final few minutes when Jones unwittingly turned in Mata's angled shot before Rafael was shown a straight card for a challenge on Luiz that sparked a melee between both sets of players.
Ferguson was angry at Luiz's reaction to Rafael's challenge near the corner flag, accusing the Brazil defender of play-acting and going down like a "dying swan." Luiz appeared to be smiling as he lay apparently injured on the ground, increasing United's sense of injustice.
Ferguson was just as unhappy with his team's laboured display, with his decision to rest Wayne Rooney, Rio Ferdinand, Michael Carrick and David de Gea and give some fringe players an opportunity backfiring. The team already appeared to have turned its sights to next season, failing to score at home for the first time in 67 matches.
"We expected a better performance," Ferguson said. "It was difficult for players coming in. Chelsea had everything to play for."
Playing its 65th match of a grueling campaign, Chelsea was still more sprightly than United and went close through Oscar, whose first-half shot struck the post, before benefiting from a late touch of fortune.
"It's a very important win. It was like a final," Mata said. "We deserve to play in the Champions League next season. If we play together like we did today, I think we can do it."
United cannot now beat its previous best points total in a season of 92, but is still 13 points ahead of City.
The biggest flashpoint in an otherwise uneventful Merseyside derby was a decision to rule out Everton defender Sylvain Distin's headed goal in the second half after an apparent foul on Liverpool goalkeeper Pepe Reina. There appeared minimal contact with Everton striker Victor Anichebe, however.
"You people (media) are quick to remind me I've not won at Anfield but if you don't get any decisions at Anfield, it makes it very difficult to win," Everton manager David Moyes said. "It is quite a regular occurrence when you come here."
Liverpool defender Jamie Carragher kept a clean sheet in his 30th and final derby before retiring at the end of the season. His team is five points behind Everton and almost assured of finishing the campaign seventh.