Played in front of an impressive crowd of 1,671, the game remained goalless until four minutes from time when Adnan Januzaj curled a free-kick into the top corner.
Two minutes later it looked like we'd secured a point as Nathan Oduwa challenged Anders Lindegaard, won the ball, took a moment and fired into the top corner.
But it wasn't to be as Thorpe rose well to meet Januzaj's corner and power home the winner in the second minute of injury time.
Januzaj and Lindegaard provided the experience in United's line-up alongside striker James Wilson while Connor Ogilvie returned to action after injury for us with Cristian Ceballos also back in the starting line-up.
The game was played at a real pace throughout but despite plenty of enterprising football, chances and efforts at goal were at a premium.
The closest either side came to breaking the deadlock in the first half was when Oduwa latched onto Emmanuel Sonupe's cross, turned away from Saidy Janko and curled just over.
Daniel Akindayini headed just wide on eight minutes, Wilson shot straight at Luke McGee after a scramble on 11 minutes and Oduwa's curler followed a minute later.
Ceballos did well stooping to angle a header just over midway through the half and Andreas Pereira's shot from Januzaj's cross looked on target but Dominic Ball was there to block.
That was the story for the rest of the half in terms of chances as Sonupe's well-struck effort from the edge of the box was blocked by Thorpe and Josh Harrop threw himself in to deny Alex McQueen just before the break. That cost the midfielder though as he was injured making the block and limped off, replaced by Joe Rothwell.
We started brightly in the second half and forced two early saves from Lindegaard – Ceballos' low drive dipped just in front of him but was comfortable, but he was at full stretch to turn aside Oduwa's 20-yarder two minutes later.
The next effort of note came in the 73rd minute when Januzaj clipped a free-kick over the defensive wall but a yard wide.
The winger went one better four minutes from time when he found the top corner from the right of the penalty area.
We hit back straight away as Oduwa was rewarded for his efforts on 88 minutes but the team's joy was short-lived as Thorpe delivered the knockout blow.
There was still time for one more attack as Ceballos jinked into the box only to lash over from 16 yards.
Spurs U21s: McGee; McQueen, Ball, Veljkovic, Ogilvie (Lesniak, 46); Onomah, Winks; Sonupe (Miller, 59), Oduwa, Ceballos; Akindayini (Lameiras, 77). Substitute (not used): Voss (GK).
Manchester United U21s: Lindegaard, Janko, Thorpe, Vermijl, Evans; Harrop (Rothwell, 45+1), Pearson; A Pereira; Wilson (Grimshaw, 46), Keane, Januzaj. Substitutes (not used): O'Hara (GK), Tuanzebe, Weir.