Dirk Kuyt scored twice in the first half and again in the 65th to complete his first hat trick for Liverpool, ensuring United wasn't able to capitalize on second-place Arsenal's draw against Sunderland on Saturday.
United, which grabbed a late consolation through Javier Hernandez, remained three points above Arsenal having played a game more. Manchester City, which downed Wigan 1-0 on Saturday, is four points further back in third.
Steven Fletcher's late header earned Wolves a deserved draw against Spurs, whose England striker Jermain Defoe scored twice for his first goals of the season. Tottenham drew level on points with fourth-place Chelsea, which visits Blackpool on Monday.
United, whose defense looked creaky at Anfield without center backs Nemanja Vidic (suspended) and Rio Ferdinand (injured), has now lost three of its last five matches to keep the title race wide open.
Manager Alex Ferguson, facing a charge of improper conduct after his criticism of a referee following the 2-1 defeat to Chelsea on Tuesday, refused to speak to the media after the game but Liverpool manager Kenny Dalglish was more than happy to.
"We know it's a good victory for us,'' said Dalglish, whose side moved above Bolton into sixth, six points behind Chelsea and Tottenham but having played more games.
"We know Manchester United are a great benchmark but our season is not finished. We want to keep going.''
Luis Suarez wriggled past three defenders to set up Kuyt for his close-range opener in the 34th, and the Netherlands forward nodded in his second five minutes later after Nani had made a hash of his clearing header, instead diverting the ball back toward his own goal.
Kuyt completed the haul by tapping in the rebound after Edwin van der Sar failed to hold Suarez's free kick, giving the Reds enough breathing space to allow them to throw recent record signing Andy Carroll off the bench for his debut.
"To make a hat trick against United is the best feeling ever. I have to thank Luis Suarez because he played great today and created two of the three goals,'' Kuyt said.
"We showed that we can compete against the best but we need to compete against the other sides.''
Ryan Giggs had a quiet match on his club-record 607th appearance for United, but the veteran winger did at least set up Hernandez late on for the Mexico striker's 10th league goal of the season.
Fletcher's goal, when he rose to meet Matt Jarvis' cross three minutes from time, denied Spurs a win that would have lifted them above Chelsea, dealing them a blow in their bid to qualify for the Champions League for a second straight season.
"It's a blow,'' Tottenham manager Harry Redknapp said. "It looked like we got three points and I hoped we'd won. I thought we deserved to win - we got three fantastic goals, amazing strikes - and had chances to kill it off.''
Defoe canceled out Kevin Doyle's opening goal in the 20th with two sensational long-range strikes in the space of five minutes to end his drought this season. They were his first goals since April last year.
Doyle equalized from the penalty spot in the 40th for his second of the game, but Roman Pavlyuchenko put Spurs back in front before Fletcher's late strike.
Redknapp could at least celebrate the return to action of star winger Gareth Bale, who came on as a substitute for the final 20 minutes having missed the last six weeks with a back injury.
The point kept Wolves second from bottom, but the central England team is now two from safety and on current form looks too good to go down.
"It looks like being a high number of points to stay up, but with that spirit and commitment I still think we'll stay up,'' said Wolves manager Mick McCarthy, whose side has beaten United, City, Chelsea and Liverpool this season.