Chelsea's performances have been far from dazzling in recent weeks but Eden Hazard's first-half strike at Stamford Bridge was enough to ease fan fears of any end-of-season jitters and ensure they will be champions if they win their next two matches.
Jose Mourinho's side have 76 points from 32 matches, 10 more than second-placed Arsenal, who beat Reading 2-1 in Saturday's FA Cup semi-final at Wembley.
United, whose run of six straight league wins came to an end despite dominating the play against a defensive Chelsea, remain third on 65 points but rivals Manchester City could move a point behind them if they beat West Ham United on Sunday.
"We are focused on us, we have six matches to play," Mourinho told Sky Sports. "The game was exactly the game we want.
"The only thing we couldn't do was to kill the game with a second goal. We were able to make their important players disappear. Nobody saw them. They were in our pockets."
Elsewhere, Leicester City claimed a third successive Premier League victory and moved off the bottom thanks to a 2-0 home win against Swansea City.
Burnley are the new basement side after a 1-0 defeat at Everton, while Stoke City beat Southampton 2-1 and West Bromwich Albion triumphed 2-0 over Crystal Palace.
UNITED UNDONE
United made a confident start despite missing a number of defensive players because of injury and being forced to play Wayne Rooney in midfield.
However, their hard work was undone when Hazard collected Oscar's neat backheel and cut in from the left to score after 38 minutes.
Chelsea, who last won the league in 2010, were looking to exploit United on the counter attack and Hazard flicked a shot onto the crossbar at the start of the second half after Didier Drogba's initial shot deflected off defender Chris Smalling.
Radamel Falcao hit a left-footed drive against the outside of the post as United pressed for an equaliser but Chelsea held on to ensure victories in their next two matches against Arsenal and Leicester, a game in hand, will give them the title.
Leicester's survival hopes have looked bleak for most of the season and they have been bottom since November but they faced Swansea full of confidence after back-to-back league victories.
Leonardo Ulloa's first-half goal set Leicester on their way before Andy King added a second late on to move Nigel Pearson's side up to 18th, level on 28 points from 32 matches with Hull City, who are outside the drop zone only on goal difference.
BASEMENT BURNLEY
Struggling 10-man Burnley had no such luck in their bid for survival as they sunk to the bottom of the pile on 26 points from 33 games after a 1-0 defeat at 12th-placed Everton.
Everton's Ross Barkley missed an early penalty but Kevin Mirallas made amends before Burnley's Ashley Barnes was sent off for a second bookable offence at the end of the first half.
Queens Park Rangers, who like Hull do not play this weekend because of the FA Cup semi-finals, are second-bottom and level on points and number of games with Burnley.
Stoke City claimed their first victory in five matches and moved up to ninth after coming from behind to beat sixth-placed Southampton 2-1 at the Britannia Stadium, hurting the visitors' hopes of Champions League football.
Tony Pulis's return to Crystal Palace as West Bromwich Albion manager was a happy one as his side won 2-0 and ended a run of three straight defeats.
Goals from James Morrison and Craig Gardner at Selhurst Park look to have guaranteed West Brom's Premier League status as they are 13th with 36 points. Palace remain 11th with 42 points from 33 matches.
(Editing by Mark Meadows)
