They had been second best to Liverpool for long periods and when they had Paul Scholes sent off with four minutes left, a point was surely the best they could have hoped for.
But in injury time John O'Shea blasted home in the six-yard box with what was United's only shot on target in the whole match.
It was so crucial. The United fans celebrated as if they had won the title and their players were soon to join in after surviving a stunned Liverpool's attempts to fight back in the dying seconds.
• Sir Alex hails 'massive result'
Liverpool manager Rafael Benitez was true to his word that he would not flinch from fielding a very strong side against the Premiership leaders.
Benitez had all his big guns back and even risked Peter Crouch on the bench despite his broken nose and the need for an operation next seek. Steve Finnan played his 400th career league game.
But that is a little short of Ryan Giggs' remarkable 700 matches for United, who opted for Henrik Larsson up front and Louis Saha on the bench.
The opening was tense and scrappy, and the first decent effort was a 25-yarder from Daniel Agger that dipped over Edwin van der Sar's bar on 12 minutes.
A minute later United put together a fine move, instigated by Giggs who gave Patrice Evra the chance to chase to the line and cross for Cristiano Ronaldo to stab wide at the near post.
Then Finnan crossed for Mark Gonzalez to send in a header that Edwin Van der Sar saved to his left.
Liverpool used Steven Gerrard largely on the right, hoping he could drift inside to support Xabi Alonso, but it served only to give Scholes too much room and the United man dictated much of the play.
Ronaldo burst through to fire over, Scholes having set up the play, before at the other end Craig Bellamy saw an effort deflected away off Nemanja Vidic.
A tapped free-kick then saw John Arne Riise fire a left-footer inches wide from 20 yards.
Liverpool started to peg United back into their last third and one chance created by Bellamy after he had robbed Vidic somehow eluded Dirk Kuyt in the six-yard box.
Bellamy's pace continued to give United trouble, while Gonzalez fired in a 20-yarder that Van der Sar held.
But the dangers of United on the break were all to evident. Wayne Rooney and Ronaldo were an increasing threat, and Alonso got himself booked for kicking the ball away on 40 minutes after incidents with both United men.
Two stunning tackles by Jamie Carragher followed on Ronaldo and then Rooney, while Michael Carrick was cautioned for holding back Riise.
Gerrard and Bellamy both had good chances in the opening minutes of the second half, before Bellamy had a close-range effort ruled out for offside.
Bellamy and Kuyt both had efforts blocked, and then Riise fired a 20-yarder just over the angle.
But United responded with breaks of their own, Ronaldo prominent, and on the hour Liverpool replaced Gonzalez with Fabio Aurelio.
United soon took off Evra and sent on Mikael Silvestre as both teams now had more more defensive players on the pitch, such was the delicate balance of the match.
Then United made a positive move, sending on the speedy Saha for Larsson, the Swede in his final league match for the club before his loan ends.
After 68 minutes Jermaine Pennant replaced Bellamy, who had run selflessly all match, and Gerrard was pushed forward.
United lost Rooney after a foul by Carragher that cost the Liverpool man a booking. Rooney had damaged his knee and limped away to be replaced by O'Shea.
Crouch was then sent on for Mohamed Sissoko and on 80 minutes Neville was cautioned for bringing down Pennant.
Crouch found space at the far post, but when a header seemed his best chance of scoring, he opted to bring the ball down and volley, van der Sar saving well to his left.
Four minutes from time Scholes managed to get himself sent off for swinging and missing Alonso with a right hook. The Spaniard had been holding the United man's arm and having already been booked, he was fortunate not to receive a second yellow card.
Van der Sar saved superbly from a Crouch shot, but in injury time United stole the points when O'Shea scored after a Ronaldo free-kick had rebounded off Jose Reina.
The goal stunned Anfield, who had seen their side dominate much of the second period but without adding the finishing touch.
For United, it will be a result savoured for years, one that almost certainly gives them the title.
Sir Alex hails 'massive result'
Sir Alex Ferguson claimed Manchester United were lucky to beat Liverpool - and
admitted the referee was right to send off Paul Scholes for violent conduct.
The Manchester United manager believes the last-gasp win over Liverpool at
Anfield was a 'massive result' in the title race.
'Liverpool will feel very unlucky and they deserve to. It was a fantastic
result. We had a lot of narrow escapes and Liverpool upset our rhythm.
'It is a massive result for us. We broke away late on against Fulham and
scored and now we`ve done it here. We`ve had that bit of luck in the last two
weeks but you need luck if you are to win titles.'
The Scot is still not ready to celebrate the title however.
'There is a 12-point difference but I don`t think anything is impossible in
modern-day football. In 1998 we had a great lead going into an Arsenal match but
we had some terrible injuries. The pool then was nothing like as strong as it is
today though. That helps us.'
United midfielder Scholes was sent off with four minutes left after swinging
an arm at Xabi Alonso and will miss three games.
Ferguson told MUTV: ' I've seen it, he's lifted his hand and you can't do
that. I think the referee [Martin Atkinson] got one right in terms of intent.'
Striker Wayne Rooney hobbled off clutching his thigh after a high tackle by
Jamie Carragher. 'We have to get him scanned but it's a bad tackle around the
knee. We will have to judge it with the game [Lillle in the Champions League]
coming up in midweek,' said the United boss.
Liverpool boss Rafael Benitez looked stunned by the defeat. He said: 'I would
have trouble explaining how we lost that in Spanish; in English I find it almost
impossible.
'We dominated the game, were in control and had plenty of attacks. Sometimes
football is all about luck. When you have so much of the play and make chances
without scoring, you must be careful against a team as good as United.
'United have a great defence and a fine goalkeeper. He stopped one from Peter
Crouch at the end everyone felt was going in. But although we had so much of the
game, we did not make too many chances.
'The decision to disallow Craig Bellamy's effort in the first half for
offside was right. It just was not our day.'
He added: 'United are really close to the title now. Chelsea are a good team,
but they cannot make mistakes now because United will continue to win.
'As for us, we are down now, but we will train hard and be ready for
Barcelona on Tuesday.'
Liverpool 0 - 1 Manchester United
