Chelsea struck first as an awful Steven Gerrard blunder set them on their way to an ultimately comfortable Anfield win that took them to 83 points and also ended Liverpool's outside hopes of finishing fourth.
United responded as Nani's first-half goal proved enough to get past Sunderland and take them to 82.
In next Sunday's final round of fixtures Chelsea host Wigan Athletic, who beat them last September, while United are at home to Stoke City. Chelsea's superior goal difference of nine means that for United to retain their title they must win and hope the Londoners lose or draw.
Although Chelsea will look back on Sunday's game as an unexpectedly easy victory, Liverpool were on top for the first half hour as Alberto Aquilani went close twice.
Chelsea had shown almost nothing in attack but were then gifted a goal by Gerrard.
The England midfielder, who was on the brink of moving to Chelsea five years ago delivered a totally unnecessary long-distance back-pass that was easily intercepted by Didier Drogba. He rounded Pepe Reina with ease and rolled the ball into the empty net after 33 minutes.
LAMPARD GOAL
The goal changed the whole atmosphere of the match and within nine minutes of the restart it was 2-0 as Frank Lampard swept in his remarkable 21st league goal of the season.
Liverpool's extra-time exertions on Thursday against Atletico Madrid in the Europa League semi-final then kicked in as what had appeared an immensely dangerous penultimate fence for Chelsea was eventually cleared while barely breaking stride.
It was Chelsea's first league win at Anfield since 2005 and leaves them firmly on course for the League and Cup double. They face Portsmouth at Wembley on May 15 in the final.
"We deserved to win. We did a fantastic job because there was a lot of pressure on us in this game," said coach Carlo Ancelotti, who is set to win silverware in his first season in charge.
"Now the team is fit and in good physical condition, good mentality ahead of next week's game. I always said the title would be decided at the end of the season."
Lampard added: "We were at a bit of a low point a couple of months ago but we dug ourselves out of it and pushed on to be on the brink of doing the double."
United, who had not lost to Sunderland in the league for 13 years, took a while to subdue them on Sunday before Nani drove in a nicely-angled shot after 28 minutes.
Dimitar Berbatov disappointed again, missing two great chances, while Michael Carrick had a shot cleared off the line, leaving United to survive a nervy second half as Sunderland probed for an equaliser, although without really threatening to find one.
"We missed an awful lot of chances, 1-0 is not a healthy score away from home," United manager Alex Ferguson told Sky Sports.
"They probably felt they were comfortable but we got there though, that's the important thing."
Looking ahead to next Sunday and United's bid for an unprecedented fourth
