United went in front just after the half-hour mark. Spurs failed to clear their lines when playing inside their own box, and when the ball came back in courtesy of an Amad Diallo cross, Bryan Mbeumo slipped behind Pedro Porro to head in at the far post.
Tottenham nearly pulled level on the other side of half-time when Cristian Romero flicked on a Wilson Odobert cross, only for Senne Lammens made a fine save with his feet. Moments later, the Belgian threw up a strong hand to bat away a half-volley from Joao Palhinha.
Spurs had the ball in the net through Brennan Johnson but the flag was quickly raised for an obvious offside as the hosts continued to push for an equaliser. With only six minutes to go, United finally caved in. Odobert skipped past Manuel Ugarte with ease before teeing up Destiny Udogie to put in a low cross, which was received by Mathys Tel and finished on the swivel by the Frenchman.
What became a manic end to the game opened up for Benjamin Sesko to find a winner when slipped through by Mason Mount, but the Slovenian dawdled on the ball too long and was tackled at the last by Micky van de Ven. Sesko walked away from this challenge injured and had to hobble off, but as United had used all their substitutes, they had to finish the match with 10 players.
Entering six minutes of added time, Tottenham turned the game around completely. United couldn't clear from a Spurs corner, with the ball falling to Odobert on the edge of the box. The Frenchman curled an effort back in, which was flicked on by Richarlison and past a helpless Lammens.
Yet there was still time for one final twist. United won a corner, which sailed to the back post for De Ligt to nod over the line by a matter of inches and save a point. The result means both sides missed the chance to climb to second in the Premier League table before Manchester City's meeting with Liverpool on Sunday.
GOAL rates United's players from Tottenham Hotspur Stadium...
Senne Lammens (7/10):
Started off nervily by letting a pass from De Ligt roll under his foot and out for a corner but recovered well with a series of saves.
Matthijs de Ligt (7/10):
Had some early trouble watching Richarlison's marauding runs from the left, though the Dutchman quickly figured the Brazilian out in that regard. Saved the day with one of the most important headers of his United career.
Harry Maguire (7/10):
A rock at the back. Stifled Randal Kolo Muani before his half-time substitution and did the same to Richarlison afterwards. Withdrawn with a minor injury for Yoro. No surprise it all went to pot after his substitution.
Luke Shaw (6/10):
Protected by Dorgu so well that there was little on Shaw's plate to clean up, even despite Spurs seeing more of the ball.