Rafael Benitez's side came from behind in an explosive clash at Old Trafford to move within four points of leaders United, who still have a game in hand on their bitter rivals.
Cristiano Ronaldo's 23rd minute penalty gave United the lead, but Fernando Torres capitalised on a mistake by Nemanja Vidic to equalise five minutes later.
Steven Gerrard scored from the spot to put Liverpool in front in the 44th minute after the England midfielder was fouled by Patrice Evra.
In the 77th minute, Vidic was sent off for hauling down Gerrard and Fabio Aurelio scored from the resulting free-kick.
Andrea Dossena completed a memorable day for the Reds when he lobbed in the fourth in the 90th minute, handing United their biggest home defeat since QPR ran riot at Old Trafford on New Year's Day 1992.
"We knew we had to win," Benitez said. "We have played better, but not against teams at the level of United so I am really pleased for the players.
"The league is very difficult but at least we now have more options and we are more confident that we can beat anyone and stay closer."
United manager Sir Alex Ferguson added: "It is a hard one to take because I thought we were the better team and the score does not reflect that.
"If the league was starting today, you would take a four-point start. Now the thing is to respond."
Arsenal moved back into fourth place with a 4-0 win over Blackburn at the Emirates Stadium.
The Gunners climbed above Aston Villa thanks to Andrey Arshavin, who scored his first goals for the Gunners since his January move from Zenit St Petersburg.
Arshavin deflected in Theo Walcott's second minute cross and struck again in the 62nd minute with a superb solo effort.
Emmanuel Eboue scored with three minutes to go and the Ivorian also drove home a penalty in the final seconds.
Everton remain in the hunt for a top-four finish after beating Stoke 3-1 at Goodison Park.
Brazil striker Jo, on loan from Manchester City, opened the scoring in the 18th minute with a neat finish from Marouane Fellaini's pass.
Relegation threatened Stoke fell further behind when Joleon Lescott tapped in after 24 minutes.
Stoke got a goal back through Ryan Shawcross in the 52nd minute but Fellaini sealed the points in the 90th minute.
Struggling Newcastle remain in trouble after drawing 1-1 at Hull.
Hull made a dream start when Geovanni headed home Craig Fagan's cross in the ninth minute but Newcastle, who had Michael Owen back from injury, equalised through Steven Taylor's 38th-minute volley.
Middlesbrough striker Marlon King rescued a 1-1 draw against relegation rivals Portsmouth at the Riverside Stadium.
Paul Hart's visitors took the lead when Peter Crouch volleyed home from the edge of the penalty area in the 30th minute.
Middlesbrough, who sit second bottom of the table, were reduced to 10 men late in the second half when Matthew Bates was sent off for a second yellow card after diving.
But King struck in stoppage time to salvage a vital point for Gareth Southgate's team.
Fulham defeated Bolton 3-1 at the Reebok Stadium to record a first away league win this season.
Andrew Johnson took advantage of a mix-up between Andy O'Brien and Jussi Jaaskelainen to score Fulham's opener in the 42nd minute.
Gary Megson's team equalised three minutes later when Kevin Davies fired past Mark Schwarzer.
Simon Davies restored Fulham's lead in the 56th minute with a close-range effort and Diomansy Kamara added a third in the 88th minute.
Wigan snatched a controversial 2-1 victory at Sunderland.
Ben Watson opened the scoring with his first goal for Wigan in the 12th minute, driving home a low drive from 20 yards.
Sunderland levelled thanks to Grant Leadbitter's 41st minute strike but Wigan got the winner on the stroke of half-time.
With Sunderland appealing for play to be stopped after Kenwyne Jones went down with a head injury, Charles N'Zogbia ran through to score.
On Sunday, Chelsea, seven points behind United, can keep alive their title hopes with a win at home to Manchester City. Aston Villa host Tottenham and West Ham face West Brom on Monday.
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