Robin van Persie ended his two-month goal drought by slotting in a penalty for United on a day of jubilant celebrations involving managers.
The Netherlands striker hugged manager Alex Ferguson and lifted him into the air after converting a 66th-minute spot kick to wrap up a dominant win, sparked by Michael Carrick's early goal at Britannia Stadium.
"He nearly killed me — he forgets I'm 71!" a smiling Ferguson said. "It was a great celebration as it brought the emotion of the players and the fans together. We really did celebrate that."
United restored its 15-point lead at the top over City, which has long given up hope of defending the league title. But Roberto Mancini's team moved closer to salvaging its season by holding off Chelsea in an entertaining FA Cup semifinal after goals from Samir Nasri and Sergio Aguero.
City will be a big favourite against Wigan in the final, and a second cup title in three years would take some of the sting out of surrendering the Premier League to its crosstown rival.
"It is another great day for the club," City captain Vincent Kompany said. "We never doubted the fact that we wanted to win trophies. This was an important game and it will be an even more important game in the final against Wigan. That is what we are looking forward to now."
A day after Wigan's victory over Millwall was marred by infighting between Millwall fans in the stands, the game between City and Chelsea was all about entertaining football, full of free-flowing attacks and missed chances.
Demba Ba pulled Chelsea back into the game with an acrobatic finish in the 66th minute, and manager Rafa Benitez was left fuming over a penalty appeal after Fernando Torres was brought down by Kompany in the area shortly afterward.
"I'm disappointed because we could have scored another goal, we had one or two clear chances," Benitez said. "The main one is the penalty not given. The consequences could have been a red card and a goal for us, and it could have changed the game."
The revelry of Van Persie and Ferguson at Stoke was nothing compared to that of exuberant Sunderland manager Paolo Di Canio, who celebrated all three spectacular goals in his team's vital 3-0 win at northeast rival Newcastle with show-stopping theatrics on the sidelines.
By delivering repeated fist pumps, sliding on his knees and joining in group hugs after goals by Stephan Sessegnon, Adam Johnson and David Vaughan, Di Canio demonstrated the passion and enthusiasm he's been asked to instil in players for the run-in.
"It's the second pair of trousers I've lost — but I would like to lose my trousers every weekend. I would lose all my money, to be honest," said Di Canio, who won his first match as Sunderland manager after opening with a loss at Chelsea last weekend.
"I wanted to go further, but I couldn't because I am too old. I have only 20 yards in my legs now — that's why I fell down."
The situation at the bottom is getting increasingly tight. Reading and Queens Park Rangers are all but relegated and Wigan is third from bottom, three points below Sunderland, Stoke and Aston Villa but having played two games fewer.
It's another story at the top.
The way it is heading, United is likely to be celebrating a 13th Premier League title either at home to Aston Villa on April 22 or away at Arsenal on April 28 and is on course to match or beat Chelsea's record haul of 95 points from the 2004-05 season. United has 80.
"At the end of this season, United deserve to win this title," Mancini said.
The win over Stoke was United's 26th in 32 games and was never in doubt from the moment Carrick prodded in from close range in the fourth minute after a spot of pinball in the penalty area following Van Persie's in-swinging corner.
With Wayne Rooney prompting play in the unusual position of central midfield, United always carried a threat but needed Van Persie's penalty to finally see off Stoke, which has now won just one of its last 14 games.
"It was relief but it was an important time in the game," said Van Persie, who had gone nine games without a goal stretching back to Feb. 10. "I had to score that one and thankfully it went in. The relief of a couple of weeks came out I would say."
While Stoke manager Tony Pulis stormed out of his post-match news conference, Ferguson was enjoying a 900th win in nearly 27 years as United manager.
"It's not so much the points — our responsibility at Manchester United is to go out and win every game," Ferguson said. "I don't think supporters at our club think any different.
"This was the start. We have six games left, go and win the next one. That is what we want to do."
AP Sports Writer Mattias Karen contributed to this report.