Clint Dempsey struck two minutes into injury time for Tottenham to rain on Robin van Persie's parade at White Hart Lane.
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Van Persie had put Manchester United on course for a vital win when he scored his sixth goal against Spurs, but after a sustained period of pressure, Dempsey delivered Andre Villas-Boas' men a thrilling equaliser with less than 60 seconds of the match remaining.
The American, who had missed a gilt-edged chance earlier in the second half, got on the end of Aaron Lennon's pull-back and slotted home after David De Gea's weak punch.
The draw means United are now just five points ahead of Manchester City after Roberto Mancini's men after their win over Fulham on Saturday.
For so long this seemed like it was going to be one of the disciplined no-frills victories that have been so key to helping Sir Alex Ferguson win his 12 titles.
Van Persie, who was making his first appearance in north London since his summer switch from Arsenal, took advantage of some sloppy marking from Kyle Walker to nod home a 25th-minute opener, and the away side looked comfortable thereafter.
Villas-Boas had challenged his men to prove they were serious top-four contenders by beating their esteemed visitors, and for the majority of the match they failed to deliver.
Their passing was often poor while Jermain Defoe and Dempsey both missed good opportunities, yet that counted for nothing come the final whistle after the heart-stopping equaliser went in.
Despite heavy snowfall in the capital overnight, the game went ahead after a late pitch inspection.
Tottenham settled the better of the two sides, getting into their rhythm on what was a bitterly cold afternoon in the capital.
United barely had a touch in the first 10 minutes, but De Gea remained untested. Scott Parker raided the United midfield to win the ball and drive at goal, but he could only curl over the bar.
Van Persie managed to peel off his marker and meet Phil Jones' cross at the back post but Hugo Lloris saved the Dutchman's header with ease.
Lennon flew up the other end and drove low at De Gea, who palmed it into Defoe's path, but the England striker was ruled offside.
Michael Carrick's late tackle on Dempsey earned him a booking and gave Tottenham a free-kick 25 yards out. Gareth Bale swung the set-piece into the back post but the cross was just too high for Steven Caulker.
Spurs' fans remained upbeat despite the freezing conditions, but the atmosphere soon turned sour when United took the lead.
Danny Welbeck found Tom Cleverley and he whipped in a perfect cross for Van Persie, who lost Walker and nodded past Lloris.
The hosts almost hit straight back through Defoe, who stung De Gea's palms with a powerful drive.
Tottenham lacked ideas going forward and the home crowd started to turn on their team.
They upped their game just before half-time, though. Bale thundered a powerful volley which De Gea did well to save just before half-time and Lennon was denied a run at goal when he was hacked down by Patrice Evra.
Spurs flew out of the blocks after the re-start. Defoe drifted in from the right flank and shot just wide of De Gea's goal and Bale curled an audacious shot just over.
Dempsey should have equalised in the 52nd minute when he picked up Mousa Dembele's pass following a mazy run by the Belgian, but De Gea saved with his legs.
Parker was denied a free-kick near the United box, much to the dismay of Villas-Boas. Ferguson then aimed his ire at Chris Foy after the referee failed to award United a penalty when Wayne Rooney, who had come on after 60 minutes, went down in the Spurs box.
Defoe managed to wriggle into the box and his blocked shot fell to Dempsey but he shot wide.
Walker sped down the right and delivered a wicked cross for Caulker, but he again could only steer his effort wide of goal.
Bale looked the most likely to break the United defence. The Welshman used his pace to create some space for Defoe, but he took one touch too many and Nemanja Vidic stole in.
A powerful shot from Bale clipped Ferdinand and sailed inches wide as Tottenham's bid for a point looked like ending in failure.
Yet with two minutes and four seconds of the three added minutes gone, Dempsey popped up in the box and stabbed home after De Gea had flapped at a cross.