The Cobblers were facing a side who had been in FA Cup action away at Maidstone less than 48 hours previously and took advantage thanks to Marc Richards early goal.
Stevenage gave as good as they got, however, and had chances to level throughout a hard-fought contest.
In form striker Ivan Toney was summoned from the bench with just over half-an-hour remaining as Chris Wilder looked for his side to make the game safe.
A second goal was elusive though and the majority of the 4,431 crowd had some nervous moments, notably Lee Barnard's shot against the bar, before the final whistle signalled an important win for the hosts.