Kenny McEvoy showed real composure to slot home a one-on-one chance past former Barcelona goalkeeper Victor Valdes on 26 minutes only for Rafael da Silva to level with a moment of magic six minutes later, lofting the ball over Luke McGee from 30 yards.
United's line-up most notably included striker Radamel Falcao, Rafael, Valdes and James Wilson.
However, Bongani Khumalo and Cameron Carter-Vickers kept Falcao quiet all night and Carter-Vickers came closest to a winner in the second half when his header came back off the crossbar.
United started with real intent in the first half without creating a notable chance and we had the first effort on goal when Grant Ward curled a free-kick over from the edge of the box.
Sean Goss drilled just wide from Falcao's set-up on 15 minutes and the Colombia striker just failed to meet Joe Rothwell's cross a minute later. From the corner, Andreas Pereira curled straight at McGee.
The game was starting to open up and we almost cashed in on 19 minutes as Ward chipped a pass in to Shaq Coulthirst, who shrugged off Tom Thorpe but blasted over from the left angle.
Shaq Coulthirst on the ball (picture supplied by Manchester United FC).
The opener arrived on 26 minutes. Rothwell tried a cross-field pass from the right-back position, McEvoy read it, intercepted and was through on Valdes. The young Irishman was calmness personified to place the ball in the corner.
That sparked a bright spell and we soon had two chances in a matter of seconds on the half-hour mark. Will Miller drifted in off the left to find Ward, who slipped as he shot. However, Ward won the ball straight back and found Coulthirst, whose deflected effort floated just wide.
Unfortunately, United got themselves back into the game two minutes later when McGee's throw out was picked off by Rafael and the full-back showed the presence of mind to lob the ball back over the goalkeeper's head and home from 30 yards.
Miller volleyed our final chance of the half wide before Pereira fizzed a shot over from 25 yards.
Play switched from end-to-end as the second half started brightly, Pereira again looking to strike from distance on 51 minutes, this time straight at McGee.
We came close to restoring our lead on 56 minutes when a clever free-kick from Ward found Coulthirst, who set McEvoy away down the right. He chipped in a cross, met by a glancing header from Carter-Vickers that came back off the crossbar.
A minute later, Ward got down the right and his cross came out to Miller, who volleyed straight at Valdes. Wilson responded at the other end, a 20-yard dipper gathered by McGee and then Coulthirst fired wide from 30 yards.
Within seconds, Rafael presented a chance to Goss, whose shot from 14 yards hit Falcao and made it easy for our stopper.
Rafael turned provider again on 65 minutes, his cross to the near post met by Wilson but once again McGee wasn't severely tested and collected easily.
Substitute Andy Kellett's low cross evaded Falcao and Wilson on 69 minutes before Falcao was replaced by Joshua Harrop four minutes later. At the same time, Luke Amos came on for Onomah.
Rafael provided dangerous crosses just in front of Wilson and then Khumalo did well, lunging in with Pereira at the near post with 78 minutes on the clock.
Daniel Akindayini joined the action on 79 minutes but it was United pushing on now and Connor Ogilvie blocked from Harrop after he was picked out by Kellett.
There was one further half-chance in three minutes of added time as James Grimshaw's header from Pereira's corner deflected just wide.
Manchester United U21s: Valdes; Rafael, Love, Thorpe (c), James (Kellett, 63); Grimshaw, Goss, Rothwell (Tuanzebe, 85); Pereira, Falcao (Harrop, 73), Wilson. Substitutes (not used): Willock, O’Hara (GK).
Spurs U21s: McGee; Walker-Peters, Khumalo (c), Carter-Vickers, Ogilvie; Lesniak (McEneff, 87), Ward; McEvoy, Onomah (Amos, 73), Miller; Coulthirst (Akindayini, 79). Substitutes (not used): McQueen, Miles (GK).