United were 2-0 up after 19 minutes, Van Persie opening the scoring with a left-foot finish from close range for his 12th league goal of the season and Tom Cleverley adding a quickfire second three minutes later.
England striker Rooney, who was a doubt due to midweek sickness, made it 3-0 with a 59th minute tap-in before substitute Fraizer Campbell pulled one back against his old club with a header four minutes after coming on.
Manchester United now have 42 points to City's 36 while European champions Chelsea, in Japan for the Club World Cup, remained third on 29 points with a game in hand.
City, beaten 3-2 by United in last weekend's Manchester derby after an agonising Van Persie stoppage-time winner, defeated Newcastle United 3-1 at St James' Park earlier in the day to temporarily narrow the gap to three points.
Javi Garcia headed the second after a corner in the 39th minute and Toure wrapped up the points late on after Demba Ba's goal had briefly revived Newcastle's hopes.
"It would have been a gross injustice if we hadn't won today," QPR manager Harry Redknapp told Sky Sports television after Mladen Petric set up a nervous finish with an 88th-minute goal for Fulham.
"I don't know where that came from. We were careless with our final ball and didn't end up taking our chances," said Liverpool manager Brendan Rodgers. "We will have to take that as a bad day at the office and move on."
"I've seen it, it's a terrible thing to do and I expect him to be punished - it's down to the FA. I've told him it's not acceptable and whatever he gets, he and us deserve it," Moyes told the BBC.
