A share of the spoils at the Britannia Stadium saw Arsenal return to the summit on goal difference ahead of surprise title contenders Leicester City, with both clubs now boasting 44 points from 22 league matches played so far this season.
But for the second time in a matter of days Arsenal were left to reflect on whether they had gained a point or in fact dropped two after a thrilling midweek 3-3 draw with Liverpool
Earlier, Rooney -- who made his name playing for Liverpool's city rivals Everton -- marked his latest return to Merseyside by scoring the only goal of the game at Anfield.
In his first game against United as Liverpool manager, Jurgen Klopp saw his team dominate only for Rooney to punish their wastefulness with his fifth goal in four games, a close range snapshot after Marouane Fellaini had hit the bar in the 78th minute proving the difference.
It was United's only shot on target, but it was enough to give visiting manager Louis van Gaal his fourth win over Liverpool in four games and a first away victory since the 2-1 success at Watford on November 21.
"When you beat Liverpool, it is good for the fans and for the table as our competitors also lose points," said Van Gaal. "It is a big step in a good direction and I am very happy."
Victory took United to within two points of the Champions League berths and allowed them to reclaim fifth place from West Ham United, leaving Liverpool six points back in ninth place, their top-four hopes fading.
"It's a derby and you have one job -- to win it," said a disappointed Klopp.