Jon Obika and Alex Pritchard were on target to send Spurs into the interval with a 2-0 lead.
But Marnick Vermijl reduced the deficit and a Larnell Cole brace saw the United youngsters emulate the first team to claim the title.
Tottenham made the brighter start of the two sides and former Norwich loanee Harry Kane hit the post with an effort from outside the box after 22 minutes.
And they took the lead nine minutes later as Pritchard won the ball in the air and found Obika, who tapped in from close range.
Three minutes before the break it was 2-0 as the pair combined again and this time Obika was the provider. The 22-year-old intercepted the ball in the middle of the park and found Pritchard who hit an unstoppable low shot across Ben Amos.
United desperately needed a goal and they got one in the 59th minute as a through-ball cut apart the Spurs back four and the overlapping Vermijl fired home a low shot.
There was then a moment of controversy as Tottenham goalkeeper Jordan Archer brought down Cole in the box but the referee booked the young striker for diving.
Cole did not let that distract him, however, and soon after he had United level.
Jesse Lingard had the ball in the penalty area and when he was tackled the ricochet fell to Cole, who easily finished from 12 yards.
And the drama did not stop there as substitute Tom Lawrence found Cole in some space in the area with two minutes remaining and the 20-year-old slotted home to seal the win.