The young Reds were dominant in north London and took a 36th-minute lead when Jack Fletcher curled one home from the edge of the box.
But, in a highly entertaining game, the hosts hit back, as Louis Copley chipped home towards the end of the first half.
Arsenal found the first blow after the break, with Max Dowman earning and converting a penalty. United found belief and quality to get themselves back into the game. Right-back Jaydan Kamason found the all-important equaliser, thrashing one home past Jack Porter with six minutes of normal time left.
Three substitutes then combined in extra-time to put United ahead, with Jim Thwaites sending Samuel Lusale down the left wing and Bendito Mantato tapping home.