A second-half goal from centre-half Dan Seaborne, his first of the season, lifted Steven Pressley's men two places to 16th in a tight Sixfields affair that saw hosts Coventry also miss a late Callum Wilson penalty.
It was the basement club Stevenage who made a bright start, with Lucas Akins rising brilliantly to meet a Curtis Obeng cross and head against the post in the third minute. Francois Zoko also curled an eighth-minute effort narrowly wide, with Coventry largely playing on the counter attack.
Just before half-time Stevenage nearly grabbed the opener when City keeper Joe Murphy saved sharply with his legs and sought-after striker Luke Freeman slipped as he attempted to net the rebound.
The second half followed a similar pattern with Stevenage forcing the pressure. But, in the 67th minute, Seaborne arrived unmarked to meet a John Fleck corner and head the decisive goal.
Coventry were awarded a penalty with eight minutes remaining when Bira Dembele was adjudged to have handled in blocking a shot. However, 20-goal top scorer Wilson, who had scored in each of his last five games, saw his spot-kick well saved by Steve Arnold.
Stevenage heaped more pressure on the Coventry goal in the final minutes and rattled the woodwork for a second time when a deflected Filipe Morais free-kick struck the bar. But it was to no avail as Coventry took the points leaving Stevenage still two points adrift of safety.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.