United sealed a needlessly nervy 2-1 home win over eighth-placed Liverpool to maintain their seven-point lead after Van Persie with a goal and Patrice Evra with two assists put rival Luis Suarez in the shade.
In contrast, the game in London was never in doubt with City winning 2-0 for their first league win at Arsenal in 38 years.
City were given a helping hand by the 10th-minute dismissal of Arsenal's Laurent Koscielny for wrestling Edin Dzeko to the ground before James Milner and Dzeko netted before the break.
Liverpool have had to watch with horror over the last two decades as big rivals United undisputedly crowned themselves kings of the English game, trampling over the Anfield side's legacy after they had shone the brightest in the 1970s and 80s.
The first half at Old Trafford, which followed United's 2-1 win at Liverpool in September, suggested talk of the balance of power should be replaced by whisperings of the huge gulf in class such was the ineptitude of Brendan Rodgers' side.
Dutchman Van Persie, English football's in-form striker along with Liverpool's Suarez, grabbed a 19th-minute opener when he swept in Evra's cross in inimitable style.
"Robin van Persie is different class. He produces moments in the game others can't do and we are glad he is on our side," man of the match Danny Welbeck told Sky.
"We had our gameplan and it worked really well in the first half. They came into it more in the second half but we got the three points and showed our character."
Uruguay's Suarez, with 15 league goals this term, was often jeered by the home crowd in a forgettable performance where nothing went right but he took the sting out of any more vocal taunts by shaking Evra's hand before kick-off.
The arrival of the lively Daniel Sturridge at half-time for his Premier League debut after joining from Chelsea and the fact they somehow went into the break just 1-0 down boosted Liverpool's confidence in the second half.
It was soon dampened when Van Persie's free-kick was headed goalwards by Evra, prolific for a left-back with four goals this term, and the ball deflected off team-mate Vidic before bulging the net. No Liverpool players appealed for offside but replays showed the Serbian was just ahead of their back-line.
Liverpool's defence and especially Johnson had been found wanting for the goal but Sturridge dug them half out of a hole when he struck after 57 minutes when Gerrard's pil
