First year pro Nathan Kerr skippered a side which included nine scholars and another two from the bench.
On a difficult muddy pitch at Pancake Lane, it was a goal on the hour from close range that won the game for the Spartan South Midlands side.
The best chance of a goalless first half fell to Michael Cregan, who fired straight at the 'keeper and although Liam Brady and Nathan Kerr went close in the second, Boro couldn't find an equaliser.
Stevenage XI: Nolan (Gibson 82), Fraser, Wilmot, O'Keefe, Croud (Omar 82), Kerr, Slater, Brady, Etheridge (Georgiou 69), Ofosu, Cregan
Sub not used: Taylor