Midfielder strikes two minutes into added time to cancel out van Persie equalizer as United gains point to move five points clear of Manchester City at the top of the table.
The American turned the ball in from two minutes into injury time to wild scenes in the snow in north London to snatch Andre Villas-Boas’ side a point it fully deserved but had appeared unlikely to manage.
Robin van Persie had headed United ahead in the 25th minute before the visitors produced a resilient backs-to-the-wall display under a barrage of Tottenham pressure, with visiting goalkeeper David De Gea making a number of crucial saves.
The result means United’s advantage at the top of the Premier League has been cut to five points this week following Manchester City’s victory over Fulham on Saturday, while Spurs remain fourth as they chase a Champions League spot.
The build-up to the game was dominated by concerns over the snowy conditions as referee Chris Foy declared the pitch playable following an inspection just over an hour before kickoff.
Spurs made three changes to the side that drew with QPR, with Scott Parker making his first league start of the season to replace the injured Sandro, while Steven Caulker and Clint Dempsey also came into the team as Jan Vertonghen dropped to the bench due to illness.
United made just one change to the starting lineup that beat Liverpool as Phil Jones replaced Ashley Young, with van Persie and Danny Welbeck again paired in attack.
Both sides started in cagey fashion, with Spurs winger Aaron Lennon injecting some impetus into the home side's attacks as he looked to run at Patrice Evra.
Lennon nearly put Tottenham in front in the 14th minute when he burst in from the right and drilled a low, left-footed shot that De Gea saved to his left before snuffing out Jermain Defoe’s rebound.
In the 25th minute, United took the lead as van Persie headed home his 18th league goal of the season to put the finishing touch on a swift move from Sir Alex Ferguson’s side.
After some neat build-up play, Welbeck played the ball out to Tom Cleverley on the right, and the midfielder clipped in his cross to the far post, where van Persie was completely unmarked to power in with his head.
Back in north London, the former Arsenal man made sure to enjoy his celebration in front of the Spurs fans as he wheeled away to be mobbed by his teammates.
From then on, Tottenham controlled most of the game but struggled to find a way past De Gea, with the Spaniard in inspired form in the United goal.
De Gea made two sharp stops before the break, denying Defoe at the near post before brilliantly keeping out Gareth Bale’s deflected effort with his legs.
The pattern continued after the re-start as De Gea denied Clint Dempsey from point-blank range after the American went through following a silky shimmy and shuffle from Mousa Dembele on the edge of United’s area.
Yet Tottenham began to run out of ideas and was unable to find a way past United’s defense as the visitors looked to sit deep and play on the counterattack, putting bodies behind the ball and always managing to find a last ditch block or saving header.
Then, two minutes into added time, De Gea produced a weak punch that fell to Lennon. The winger kept his head to pick out Dempsey in a crowded penalty box, and the American made no mistake in slotting the ball into the bottom corner from 10 yards.