Tottenham thought they had secured all three points after Dimitar Berbatov had fired them into a first-half lead.
But Tevez broke the hearts of the Tottenham fans when he got in front of Michael Dawson to nudge home a corner from Nani in stoppage time.
Arsenal remain two points clear of United at the top following their 3-1 win at Manchester City earlier in the day, but Sir Alex Ferguson will be grateful his side managed to get something from this game.
Tottenham opened the scoring after 20 minutes when Jermaine Jenas broke clear of the United defence.
Owen Hargreaves challenged him inside the box and the ball fell to Aaron Lennon, who saw his shot beaten away by Edwin Van der Sar but Berbatov was on hand to knock the rebound home.
Van der Sar felt Jenas had handled the ball and reacted furiously to the goal being awarded with the Dutch keeper booked for dissent.
Tottenham could have doubled their lead on 35 minutes when Lennon used his blistering pace to break away down the right-hand side.
His cross fell perfectly for Berbatov but he fired his volley over the bar.
The home side had plenty of chances to extend their lead over the champions and came even closer to adding a second on 56 minutes when Berbatov played in Robbie Keane, who found himself clean through on goal but he fired his shot straight at Van der Sar.
United could have snatched an equaliser on 76 minutes when Anderson fired a low shot from the edge of the box which produced a superb save from Radek Cerny diving low to his right.
Tottenham were made to pay for their missed chances when Tevez prodded the ball in right at the death to help United come away with a valuable point.