Robin van Persie had put the league leaders 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 had gone walkabout.
The draw means United are now just five points ahead of Manchester City after Roberto Mancini's men after their win over Fulham yesterday.
Source: PA
Source: PA