Trailing to a close-range finish inside the first 10 minutes, Boro went close to equalising before the break when Ryan Loft showed neat footwork to create space inside the box, but fired over.
Henry Cowans saw a free-kick deflect over in the second half, but Boro had to wait until the final 8 minutes to turn the game on its head.
Rowan Liburd equalised on 82 minutes when he turned well in the box before firing past the 'keeper at his near post. Scholar Mickey Cregan then won the game with a minute to go, latching onto a through-ball, rounding the 'keeper and slotting home.
Stevenage XI: Trialist, Trialist, Wilmot, Johnson (Georgiou 85), Kerr, Slater, Cowans (Cregan 60), McKee, Liburd, Trialist (Ofosu 46), Loft (Cregan 60)