Robin van Persie's league-high 17th goal of the campaign gave United a 19th-minute lead, and the hosts looked likely to coast to victory at Old Trafford when captain Nemanja Vidic unwittingly deflected the ball in from close range to make it 2-0 in the 54th.
Daniel Sturridge pepped up a lethargic Liverpool when he came on as a halftime substitute and the new signing from Chelsea halved the deficit three minutes later, but Brendan Rodgers' team couldn't find the equalizer to cap its improved second-half display.
United is now 10 points clear of second-place Manchester City ahead of the champions' match at Arsenal later Sunday, with its total of 55 points after 22 games the team's highest tally at this stage of a top-flight season.
The game between England's two most successful clubs, which share 37 league titles between them, was billed by some as a duel between Van Persie and Liverpool striker Luis Suarez — the division's most prolific marksmen. Van Persie came out on top.
While Suarez was kept quiet — much to the delight of home fans who jeered his every touch as a result of his recent spats with United defender Patrice Evra — his rival continued his sensational scoring run that is keeping City at arm's length in the title race.
The Netherlands striker beat marker Daniel Agger to Evra's driven cross and calmly slotted the ball home from 12 yards for his ninth goal in his last nine games. Van Persie has also scored at least one goal in nine of his last 10 games.
"Robin van Persie is different class," United striker Danny Welbeck said. "He produces moments in the game others can't do and we are glad he is on our side."
With Liverpool's midfield giving the ball away cheaply and sitting far too deep, United was invited to attack at will and should have been more than a goal ahead at halftime.
Welbeck, given a rare start up front with Wayne Rooney still injured, thrashed wildly wide and Tom Cleverley went close with a volley. Van Persie then saw an impudent flick cleared from near the goal-line by Liverpool defender Martin Skrtel before Pepe Reina pushed the ball away from the inrushing Shinji Kagawa.
The first half highlighted the gap that has emerged between the two sides in recent years, with the last of Liverpool's 18 titles coming back in 1990. It was much different after the break, though.
Sturridge was introduced for the second half for his league debut for Liverpool and his pace and energy sparked a vast improvement by the visitors, who finally tested the United defence.
The former Chelsea striker's goal came only after United had stretched its lead, however, when Van Persie's free kick was headed down by the unmarked Evra with the ball deflecting off the side of Vidic's head into the net.
Liverpool's riposte was almost immediate, Sturridge sidefooting home from close range after David De Gea could only palm out Steven Gerrard's low shot, and it set up a tense last half hour for the home side.
Sturridge and fellow substitute Fabio Borini shot wide as United fans became increasingly anxious, and Sturridge had an even better opportunity in the 85th only to blaze over the crossbar from an angle.
United, which has made a habit of edging tight matches this season, is now 24 points clear of eighth-place Liverpool in the standings.