Chelsea extended its lead over City to six points — with a game in hand — with a 1-1 draw at Stamford Bridge, although the advantage would have been even bigger had Southampton goalkeeper Fraser Forster not produced several great saves in the second half.
Diego Costa's 11th-minute header for Chelsea, which ended his seven-game goal drought, was quickly cancelled out by a penalty converted by Dusan Tadic.
Rooney capped United's 3-0 win over Spurs at Old Trafford with a stunning solo goal and performed a boxing knockout celebration, where he shaped a flurry of punches before falling over on his back. It was a response to video footage, released by a British newspaper on Sunday, that apparently showed the England captain being floored by an ex-teammate in a sparring session at home.
"I don't know how it's got out," Rooney said. "You know, it's what friends do — we mess around in the house and unfortunately it's made the front page of the newspaper."
Marouane Fellaini and Michael Carrick also scored first-half goals for fourth-place United, which moved to within two points of Man City in what is proving to be a riveting tussle for Champions League qualification.
"We have waited a long time for such a victory," said United manager Louis van Gaal, who had come under fire in recent weeks for some insipid displays by his team.
Spurs dropped six points off the top four with a poor display that revived memories of its capitulations against the top sides last season.
In the day's other game, Everton beat Newcastle 3-0 to pull clear of relegation danger and lift some of the gloom surrounding the club. James McCarthy, Romelu Lukaku and Ross Barkley scored the goals as Newcastle finished with 10 men following Fabricio Coloccini's sending-off.
City's 1-0 loss to Burnley on Saturday made Chelsea an even bigger favourite for the league title, although Jose Mourinho's team is inching rather than motoring to the trophy. It has drawn three of its last four league matches at home.
Chelsea wasn't at its best in the first half against Southampton, perhaps experiencing a hangover from being eliminated from the Champions League by Paris Saint-Germain in midweek.
Costa headed in a cross from Branislav Ivanovic but the visitors responded with Tadic's penalty and regularly breached Chelsea's defence. It was a different story after the interval, with Chelsea repeatedly thwarted by Forster.
"If somebody tells me in August that at the end of March, we are six points in front and one match in hand, I would sign immediately," Mourinho said.
The latest incident in Rooney's colorful career may overshadow a powerful performance by United, which began a tough run of fixtures that could define its season.
United had a quicker tempo to its passing and movement, and pounced on poor defending and lapses in concentration by Spurs in going 3-0 ahead after 34 minutes.
Carrick set up Fellaini's goal with a neat pass, before sending a precise header into the corner after Fellaini caused trouble at a corner.
Rooney then seized on Nabil Bentaleb's errant sideways pass, ran straight at the visiting defence, turned Eric Dier inside out and placed a low finish past goalkeeper Hugo Lloris. He sprinted toward the corner flag, performed some shadow-boxing and then fell backward to the ground.
When Van Gaal was asked about the video involving Rooney, he said: "What is this world, twisted? I don't want to answer this question because I think it is ridiculous that we have to talk about such things."