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.
