Stevenage goalkeeper Jamie Jones was tested by Rowan Liburd's header and Garry Thompson's strike from 20 yards.
Boro's Tom Conlon had a shot over the crossbar before Jason McCarthy missed the target and Liburd had more chances.
The winner came from McCarthy's shot rebounding to Luke O'Nien, who slotted home, while Stevenage almost equalised from 10 yards though Dean Parrett.
Stevenage remain in 21st, seven points clear of the relegation zone.
Wycombe Wanderers secured a narrow win over Stevenage to move up to eighth and sit one point from the play-off places.