It was the fourth away win on the trot for the Sky Blues as they look to force their way into play-off contention.
After a poor first half, the man they had to thank was former Scunthorpe striker Leon Clarke as he returned to haunt his old club.
Clarke, who netted 11 times in 15 loan appearances for the Iron before Christmas, headed a 77th-minute winner for Coventry.
That came after skipper Carl Baker got them back on level terms on the stroke of half-time, drilling a shot back through a crowded box from a half-cleared corner and beating rookie Norwegian goalkeeper Eirik Holmen Johansen.
Scunthorpe, battling to avoid the drop, made all the early running and were ahead after eight minutes when fit-again striker Akpo Sodje met a superb right-wing cross from full-back Eddie Nolan with a close-range header for his fifth goal in nine games since joining the club.
They had Coventry firmly on the back foot but missed the chance to capitalise with a second goal.
Winger Andy Barcham fluffed one good chance and Karl Hawley missed another when he took the ball round former Scunthorpe keeper Joe Murphy but then struck the foot of a post from a narrow angle.
Murphy did rescue all three points for Coventry with a flying late save to deny Jimmy Ryan.
