Goals from Nemanja Vidic, Wayne Rooney and Dimitar Berbatov moved United into third place.
But ominously for Liverpool, United will overtake them if they win both games they have in hand on the Merseysiders.
The first 45 minutes of the game indicated that a goalless draw would be on the cards.
But as the opening period moved into injury time, the game suddenly exploded into life.
It was sparked by one of the cleverest moves that will be seen in the Premier League this season.
United won a corner on the right. Rooney trotted over and tapped the ball out of the quadrant before nonchalantly walking away.
Over strolled Ryan Giggs and his walk turned to a canter and then a sprint when he touched the ball infield and crossed to the near post where Cristiano Ronaldo headed in from close range.
The assistant referee's flag went up to indicate the corner had not been taken correctly, but the intelligent move should have been rewarded with a goal.
Giggs then stepped up again to drive the second corner into the centre where Berbatov headed the ball to the back post for the unmarked Vidic to nod the ball home from six yards.
United's second goal came in the 63rd minute and from a superb move.
Patrice Evra turned the ball to Ronaldo as he raced down the left.
The Portuguese star back heeled the ball into Evra's path, who continued his run before crossing into the centre of the Chelsea penalty area.
Berbatov produced the faintest of headed flicks and Rooney audaciously tucked his right-foot shot between Chelsea defender Ashley Cole's legs and into the net from six yards.
With three minutes to go, the Red Devils rubbed salt into Chelsea's gaping defensive wounds.
Ronaldo hammered a free-kick from the left and Berbatov met the ball at the near post with his right foot from four yards to net the third.
Ronaldo, Berbatov and Rooney could easily have added to their side's tally as Chelsea suffered their first away defeat of the season in the Premier League.
Chelsea hardly threatened the United goal with goalkeeper Edwin van der Sar's most difficult moment coming when he claimed Ashley Cole's 15th minute shot in his midriff.