Arsenal were leading 1-0 from the semi-final first leg at Emirates Stadium and United youngsters looked knocked out at 2-0 down on aggregate but came back to make it 2-1 on the night at Old Trafford and force extra-time.
United got the winner deep in extra time through 16-year-old Danny Welbeck.
After Arsenal had scored Chris Fagan gave United hope when he tapped home after a free-kick scramble in the 73rd minute and Antonio Bryan put the game into extra time when he slammed home three minutes into injury time.
Substitute Rhys Murphy scored in the last minute of the first extra period to restore Arsenal's lead but again United scored through Febian Brandy (108) and Welbeck (114).
United are away to