Both teams had taken part in thrilling 3-3 draws in midweek, but this clash looked set to be scoreless until Rooney popped up to volley home his 78th minute winner.
It was his 176th English Premier League goal, a record for a player for a single club.
The England international striker had been tied on 175 with former Arsenal great Thierry Henry.
The win lifts United to fifth place in the standings, two points adrift of Tottenham Hotspur, which occupies the final Champions League spot.
Liverpool, which had the majority of the play on its home pitch, remains in ninth spot with its fifth league defeat under Jurgen Klopp.
But the visitor had David de Gea to thank for fine stops to deny Emre Can and Roberto Firmino, while Jordan Henderson dragged a good chance wide in a drab first half.
Rooney's clinical finish after Marouane Fellaini's header from a corner rattled the Liverpool crossbar was United's first shot on target.
That statistic did not bother delighted manager Louis van Gaal, who was under pressure before Christmas after a series of poor results and lackluster performances.
"It is a big step in a good direction and I am very happy," he told Sky Sports.
"In the second-half we played much better and kept the ball better and created chances and Wayne Rooney makes the fantastic goal again," added the Dutchman.
Later Sunday, Arsenal battled to a goalless draw at Stoke City to leapfrog unheralded Leicester at the top of the EPL standings on goal difference alone.
Goalkeepers Jack Butland for Stoke and Petr Cech for Arsenal both made vital saves to keep the game scoreless, Stoke staying in seventh spot.
Arsenal, missing the injured Mesut Ozil and not risking a return for Alexis Sanchez, had the better of the possession but needed a pair of superb stops from Cech late on to keep a share of the points.
The result leaves the Gunners and Leicester tied on 44 points after 22 games, with Manchester City just a point adrift in third.