It looked as though as Robin van Persie's first-half header had given visiting United all three points until the American international intervened with one minute of the encounter remaining.
Below, Sports Mole has looked back over the 90 minutes to determine if Spurs were good value for their point.
On target 18
On target 4
Was the result fair?
The timing of the goal will leave some Man United supporters feeling that Spurs got extremely lucky. However, a quick look at the statistics will tell you that they more than deserved a draw from this match. During the last 10 minutes they were camped inside the United half and in the end they were eventually rewarded.
Better late than never! Andre Villas-Boas will not be happy with the way that his side performed during the first 45 minutes, but after the restart they really took the game to United. But for some smart stops from David de Gea, they could have easily scored before Dempsey's goal in stoppage time.
Man United's performance
For 91 minutes, there were very few faults in the United game. Granted they didn't play the slick football that they have produced at times this season, but they went about their business professionally and got the goal in the first half. Second half they defended well and looked to be heading back to Manchester with all three points until the late sucker punch.
Sports Mole's man of the match
Phil Jones: There a number of players that can claim that they deserve this award, but we are giving it to Jones. Injury has kept the 20-year-old out for a large part of the season. However, he took on the midfield responsibilities today and didn't let his team down. He kept going throughout and made a number of key challenges.
This may be harsh on De Gea, because he made a large number of great saves, but it was his timid punch that dropped to Lennon in stoppage time. The Tottenham winger then squared the ball for Dempsey to roll it into the net.
Chris Foy had a mixed afternoon at the Lane. While he allowed the game to flow and dished out warranted yellow cards, he turned down Wayne Rooney's appeal for a penalty despite the fact that he had been clearly fouled by Steven Caulker inside the area.
Tottenham: It's the FA Cup for Spurs next weekend when they travel to Championship outfit Leeds United on Sunday afternoon.
Man United: The Reds are also in FA Cup action as Fulham visit Old Trafford on Saturday evening.