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.
The visitors were a goal up after 10 minutes when Ivorian midfielder Yaya Toure split the Newcastle defence with a superb pass to Samir Nasri who rolled the ball back for forward Sergio Aguero to stroke home.
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.
QPR WIN AT LAST
Elsewhere, Queens Park Rangers celebrated their first win of the season after beating West London rivals Fulham 2-1 thanks to two-goal Adel Taarabt to end a record run of 16 matches without a victory and move off the foot of the table.
The victory stopped QPR, still five points from safety, becoming the first top-flight team since Bolton Wanderers in 1902/03 to fail to win any of their opening 17 games.
"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.
Aston Villa fans had plenty to cheer after a fighting 3-1 win at Liverpool moved them three points clear of the relegation zone and gave the Reds a reality check.
Christian Benteke scored in each half at Anfield with Andreas Weimann grabbing the other goal for Villa who were 2-0 up at half-time. Steven Gerrard headed an 87th-minute consolation for Liverpool.
"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."
Norwich City beat Wigan Athletic 2-1 while Stoke City and Everton drew 1-1.
Everton were lucky to end with 11 men after Marouane Fellaini headbutted Stoke captain Ryan Shawcross without the referee noticing in an incident that drew censure from his own manager David Moyes.
"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.
