Luke Chadwick gave The Red Devils the lead, after Ian Harte had seen his first half penalty saved by Fabien Barthez, but with under 10 minutes left, Mark Viduka ended his Premiership goal drought to earn a well-deserved point for the home side.
Indeed, Leeds will feel that they should have won the game as Wes Brown diverted Lee Bowyer`s driven centre into his own net, a carbon copy of the own goal he scored against Valencia, only for the linesman to rescue the visitors by flagging for off-side.
Sir Alex Ferguson`s side looked a different team to the one that smacked Arsenal 6-1 last week, but they were not at full strength with Roy Keane and Ryan Giggs missing, while Dwight Yorke was left on the bench after returning from the Caribbean in midweek.
Teddy Sheringham partnered Ole Gunnar Solskjaer up front and Paul Scholes moved in-field to partner Nicky Butt at the heart of the midfield with Phil Neville moving to the left.
Leeds made just the one change from the team that became the first side to win at Tottenham this season. Lucas Radebe came in for Eirik Bakke, which gave Dominic Matteo the chance to impress on the left wing and the South African taking up his more customary position at the heart of the defence.
Leeds almost broke the deadlock inside the first five minutes when Jaap Stam left Barthez short with a backpass. Robbie Keane quickly closed the French international down, but Barthez denied him with a well-timed last-ditch challenge.
The Yorkshire club continued to push forward and Viduka headed fractionally too high after Keane had got the better of Denis Irwin on the Leeds right.
Barthez then did well to tip an Ian Harte free kick over the bar as Leeds continued to apply the pressure, but United were temporarily reduced to 10 men when Phil Neville needed treatment for a cut above his right eye.
Dacourt fired wastefully high after some good work by Matteo, and Keane did likewise with the United defence back-pedalling.
The Red Devils found it hard to get into their stride as David O'Leary's side prevented United from enjoying any time on the ball. Their constant harassing of United eventually led to a booking for Lee Bowyer who was cautioned for a late foul on Irwin.
Radebe also saw yellow as he bundled Solskjaer over the touchline and, from the resulting free kick, Stam headed weakly at Martyn from Beckham's pinpoint cross.
Nicky Butt - after two previous silly fouls - became the third player booked when he brought Keane down on the edge of the box, but Harte's free kick went straight into the United wall and Dacourt's follow-up was easily gathered by Barthez.
Bowyer dragged his long range effort wide of the far post as United struggled to create anything of any note. Sheringham and Solskjaer were virtually anonymous up front and Roy Keane's presence was clearly missed with Leeds dominating the midfield.
Then, on the stroke of half time, Barthez lashed out at Ian Harte in the penalty box after dropping a deep cross. The incident was spotted by referee Graham Barber, who awarded a penalty.
David Beckham received a red card against Argentina when he committed a similar offence at the 1998 World Cup Finals, but Barthez's stupidity only warranted a caution from the whistle-happy Barber.
But Harte's spot kick was too close to the French number one who redeemed himself by diving to his right and keeping it out.
At half time, Alan Smith and Harry Kewell came on for Keane and Matteo for Leeds while Luke Chadwick replaced Butt, who had a shoulder injury, as both managers went in search of winning the match.
Neville moved to the centre of midfield with Chadwick looking to provide the penetration evidently lacking by the absence of Giggs.
The home side began the second half in much the same way as the first. United found it difficult to enjoy any sustained period of possession and were continually harassed by Leeds into giving the ball away.
Ferguson's side looked a shadow of the team that simply destroyed Arsenal 6-1 at Old Trafford last weekend and, with an hour gone, they were still to register their first shot on goal.
They had also failed to win even a corner as Leeds keeper Nigel Martyn enjoyed a quiet day in the West Yorkshire sunshine, while Ferdinand and Radebe easily kept Sheringham and Solskjaer at bay in front of him.
Suddenly, United showed exactly why they are champions by scoring a goal out of nothing.
Some neat interchanging in midfield ended when Paul Scholes fed the ball into the path of Solskjaer. His shot was spilled by Martyn and Chadwick was on hand to ram home the loose ball and give United an undeserved lead.
Martyn will certainly be disappointed with the way in which the ball slipped from his grasp, and the fact he had been unemployed for an hour beforehand may have played a part in the goal.
Sheringham, who was strangely subdued throughout the game, was then replaced by Yorke and Solskjaer almost doubled United's lead when he cut in from the left, only to shoot straight at Martyn.
Leeds struggled to get in behind a United backline superbly marshalled by Brown and man-of-the-match Stam. Kewell found it hard to get the better of Gary Neville, although he did begin to make progress, while Denis Irwin was as reliable as ever in keeping Lee Bowyer at bay.
When Kewell did eventually beat Neville, his outrageous cross was just too high for Viduka. Smith then tested Barthez from 18 yards and Kewell shot wastefully too high from distance.
Leeds continued to look for a route back into the match and Smith again tried his luck from long range, only to see it deflect wide for a corner. From the resulting flag-kick, the ball fell to Kewell who volleyed straight at Barthez, the Frenchman saving smartly.
But with under 10 minutes remaining, Leeds drew level. Mills easily got the better of Irwin on the right and his cross was flicked on by Bowyer to Viduka, who directed his header past Barthez.
It was just reward for Leeds who were the better team, but Ferguson will be fuming at the way Mills was given the opportunity to cross with Irwin in attendance.
United nearly won it when Beckham's wonderful cross found the head of Scholes, but from barely six yards, the United midfielder failed to make a decent connection and the ball was cleared.
Leeds also had a chance to win it as both sides went in search of a late winner and, in injury time, they thought they had.
Bowyer found himself in space on the right and his cross was turned into his own net by Brown. Luckily for United, the goal was ruled out as Viduka was ruled off-side, but the replays showed the decision was very harsh on the home side.
