The home side almost took the lead after just five minutes when William Edjenguele struck from close range, but it drifted just behind.
They did take the lead five minutes later, however, when David McGoldrick fired a strike into the top corner from outside the box.
Stevenage were level after 25 minutes when Robin Shroot scored his second league goal of the season with a cool finish from close range.
Chances remained few and far between as the match developed, with a McGoldrick header drifting just wide on the hour mark.
The away side grabbed the winner after 70 minutes, however, when Marcus Haber converted from close range as Stevenage moved into third spot in the table.