This was the Red Devils' worst defeat at home since their first ever Premier League game at Old Trafford - a 3-0 defeat by Everton back in August 1992.
Despite the reverse, United are still four points clear of their Merseyside rivals with a game in hand.
But too many repeat performances will have both Liverpool and Chelsea believing the title is theirs.
United, whose only dropped home points to date this season before this game came in the 1-1 draw with Newcastle on the opening day, took the lead in the 23rd minute.
Ji-Sung Park ran on to Carlos Tevez's decisive pass through the middle of the Liverpool defence.
As the South Korean rounded Jose Manuel Reina, the Liverpool goalkeeper brought him down and referee Alan Wiley pointed to the spot.
Up stepped Cristiano Ronaldo to blast his right-foot shot into the right corner of the net beyond Reina's despairing dive.
United's lead lasted only five minutes. Nemanja Vidic seemed to have an eternity to clear Martin Skrtel's long ball out of defence.
But the United defender dithered 40 yards from goal and was easily robbed by Fernando Torres.
The Liverpool striker bore down on the United goal and, as Edwin van der Sar came off his line, Torres coolly tucked the ball past the Dutchman and into the bottom corner of the net.
Worse was to come for United a minute before the interval.
Torres' precision pass found Steven Gerrard stealing in on the blind side of Patrice Evra on the right-hand side of the United box.
Evra upended Gerrard and the Liverpool skipper picked himself up to strike the resulting penalty into the bottom right corner of the net past the diving van der Sar.
United pressured Liverpool in the opening half of the second period but the final seeds of their downfall were sewn in the 76th minute.
Gerrard was hauled down by Vidic when he was set to clear the Serbian on the right corner of the United box.
Wiley had no option but to dismiss Vidic and Fabio Aurelio curled a glorious left-foot free kick beyond van de Sar at his near post and into the net.
The final indignity for the champions came a minute into injury time.
Reina's long goalkick found Liverpool substitute Andrea Dossena free on the left corner of the United penalty area and he scored with a sweet left-foot lob over the stranded van de Sar.