A 19th-minute goal from in-form striker Jermaine Beckford gave the League One leaders victory as Manchester United, who have won the Cup a record 11 times, went out at this stage for the first time since 1984.
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Holders Chelsea made sure there was no slip-up at Stamford Bridge where they crushed Championship Watford 5-0 after streaking into a 3-0 lead in 22 minutes.
Arsenal, the second most successful club in the cup's history with 10 wins, left it late to beat West Ham United in a pulsating all-London tie at Upton Park.
Goals from Aaron Ramsey after 78 minutes and Eduardo five minutes later gave the visitors a 2-1 win after Alessandro Diamanti had put the Hammers ahead just before the break.
The biggest upset of the round, and the competition, for many years came at Old Trafford where Beckford's solitary strike was fashioned by a 50-metre punt from Johnny Howson.
The ball went over the champions' defence, allowing Beckford to get a touch and angle a shot wide of keeper Tomas Kuszczak.
It was the first time Alex Ferguson had suffered defeat in the third round, the stage at which the top clubs enter the FA Cup, since he became United manager in 1986.
United's first loss to lower league opposition since 1984 also gave Leeds a memorable victory at a ground where they regularly used to duel with United for national supremacy before their slide down the leagues.
BIG SHOCK
The 9,000 away fans went wild with delight at the end of a thrilling tie which produced the first big shock of the round after a series of predictable results on Saturday.
"I must admit I didn't expect that performance," Ferguson told MUTV. "If you don't start and the other team does, you're always up against it.
"Leeds had a far bigger appetite than us for the game. You need a bit of luck and they got it but they deserved it because they played really well."
Leeds manager Simon Grayson was full of praise for his team.
"It was a good long diagonal ball from Johnny Howson and nine times out of 10 Jermaine finishes them off and that's what he did," he told ITV.
"We gave ourselves an opportunity to go and win the game from there and with a bit of luck here and there we've hung on.
"I am sure they will be celebrating in Leeds for the next few days. The players will have tomorrow off then we will start preparing for the match against Wycombe."
Grayson's men thoroughly deserved their victory which would have been more comfortable if Beckford had scored after 78 minutes instead of dragging his shot just wide.
Robert Snodgrass smashed a 25-metre free kick against the United bar two minutes later before keeper Casper Ankergren parried a goalbound effort from Wayne Rooney in stoppage time.
Michael Owen, Dimitar Berbatov and Rooney went close for United but Leeds, who needed a r
