The United States forward, who gave Tottenham its first win at United in 23 years in September, cancelled out Robin van Persie's first-half header to give the fourth-place hosts something to show for their dominance at a snowy White Hart Lane.
"Before (this season) I'd never scored against them, so it's good to help the team get results," said Dempsey, who joined from Fulham in August. "We've got a win and a draw now (against United)."
United remains top but its lead has been trimmed to five points this weekend after second-place Manchester City beat Fulham 2-0 on Saturday.
Despite salvaging a point, Tottenham fell four points behind third-place Chelsea after its London rival beat Arsenal 2-1 earlier in the day.
While United managed just five shots, Tottenham scored with its 25th shot in the third minute of stoppage time.
Dempsey swept in the winner after being set up by Aaron Lennon, who had pounced after goalkeeper David de Gea punched a shot by Benoit Assou-Ekotto inadvertently to him.
"They kept pumping the ball in the box and got their reward. You'd have thought we would have dealt with it better," United manager Alex Ferguson said. "We should have killed them off on the counterattack in the second half. It was the final ball that was letting us down."
United rarely threatened Tottenham goalkeeper Hugo Lloris after Van Persie rose in the 25th minute to meet Tom Cleverley's cross and head in his 22nd goal since joining from Arsenal in August.
"It was a good build up from Danny to Thomas and then Robin did what he has been doing all season," Ferguson said. "He notched another goal."
But Ferguson turned his fury on an assistant referee for not awarding a penalty after Wayne Rooney, a surprise substitute who only came on in the second half, was caught by Steven Caulker.
"It was definitely a penalty — he has put his leg right in there," Ferguson said. "The linesman (Simon Beck) is facing it. I thought he had a very poor game, the linesman. I thought he was disappointing.
"We have got that history with him. He never gave offside with (then-Chelsea striker Didier) Drogba at Old Trafford (in 2010) when he was three yards offside. Everyone remembers that. I certainly do."
But United had been heavily reliant on centre backs Rio Ferdinand and Nemanja Vidic, as well as De Gea's blocks, to protect its lead.
"We dominated the whole game, played well and deserved to win to be fair," Tottenham manager Andre Villas-Boas said. "We had 60 per cent possession against United ... and should have won.
"Champions like United have to go through moments like this but I think we deserved this last-minute goal."
The four points Spurs have claimed off United this season are the most since beating them twice in the 1989-90 campaign.
Despite being in control from the start, Tottenham missed the goal scoring threat of Emmanuel Adebayor, who is at the African Cup of Nations with Togo.
But danger was being created down the right flank by Aaron Lennon, who came close to scoring after 13 minutes when he burst into the penalty area and unleashed a shot that De Gea pushed away.
Van Persie's goal against the run of play didn't dampen Tottenham's spirits, with Gareth Bale's deflected shot saved by De Gea before halftime and the Wales winger also curled over after the break.
Dempsey's first chance to equalize came in the 52nd after Mousa Dembele had withstood two challenges before slipping the ball through to the striker, whose close-range shot was blocked by De Gea's foot.
"I couldn't believe he saved that," Dempsey said. "I was going to celebrate."
But while Tottenham continued to pile on the pressure, the end products lacked venom with Dempsey also seeing a tame shot easily saved on the hour.
A decisive intervention by Ferdinand prevented Jermain Defoe breaking through on goal after being released by Lennon and the centre back got his head in the way to deflect a shot from Bale wide.
But United's resistance broke down in stoppage time, just when Ferguson's United has been accustomed to stunning opponents with goals.
"Tottenham worked their socks off, you have to give them credit," Ferguson said.
United headed from the stadium to the airport and an overnight flight to Qatar for warm-weather training.
"We can get the sun cream out hopefully and get out on the beach and relax a bit," United midfielder Michael Carrick said. "It's a busy season and there are busy times ahead. It's about recuperating."