Larnell Cole struck twice in the final 20 minutes to hand the Red Devils an unlikely victory after the free-scoring away side bossed the first half to lead 2-0 at the break
Alex Pritchard was Spurs' star man in the first half, laying on the visitors' first goal and scoring the second from 25 yards out.
But United came to life after half-time, getting themselves back into the game with a goal from Marnick Vermijl and a double from Cole.
Both sides came into the game in fine form; the Red Devils beat Liverpool 3-0 while Spurs, who had scored 80 goals in their 27 previous matches this season, downed Everton to reach the showpiece.
And it was the visitors who started brightest; Milos Veljkovic went close with a curling effort early on, Jonathan Obika then hit the crossbar after beating his man at the near post, and Cristian Ceballos sent a carbon-copy of Veljkovic's shot narrowly over.
Jesse Lingard responded for United with a mazy run inside the box, but his shot was weak. Spurs were not deterred, however, and Harry Kane smashed an effort off the upright at the other end almost immediately.
The away side finally made their pressure count when United keeper Ben Amos failed to collect Ceballos' cross, allowing Pritchard to head towads goal and Obika to poke home first time.
And they doubled their lead three minutes before half-time when Pritchard picked up the ball 25 yards from goal, turned sharply and fired into the bottom corner.
United were appealing for a penalty after the break when Carroll handled Januzaj's corner, but the referee was not interested.
But they were back in the game just before the hour mark when Vermilj sprung the offside trap to latch on to Ryan Tunnicliffe's ball over the top, charge towards goal and arrow a low shot into the bottom corner from a narrow angle.
Pritchard was then withdrawn by Chris Ramsey, with Ken McEvoy, the Gareth Bake look-a-like, coming on in his place.
United's Tom Lawrence was lucky to get away with a yellow after a studs-up challenge on Veljkovic, while Ceballos tested Amos with a low drive after 69 minutes.
Referee Bobby Madley was centre of attention three minutes later when he booked Cole for diving, despite the striker looking to have been tripped by keeper Jordan Archer in the area.
But Cole was to have the last laugh, and a minute later he drew United level when the ball fell to him in the box following a sharp break, allowing him to round Archer once again and lash high into the net.
Obika missed a great opportunity to give his side the lead once more from the kick-off, lifting his shot well over the bar when through on Amos' goal.
McEvoy flashed a volley into the side netting with seven minutes on the clock after Michael Keane could only partially clear.
But Cole won it in the 87th minute follwing neat link-up play on the edge of the Spurs area, with Lawrence cutting the ball back from the byline for Cole to control and fire into the bottom corner to spark wild scenes.
United played out the remainder of the time to claim the first Under-21 title on their own turf, sparking joyous celebrations from a bumper Old Trafford crowd.