Jon Stead fired his first goal for the Sky Blues to give them the lead before Keiren Westwood saved a Gary Hooper penalty after Leon Barnett had been sent off.
Sammy Clingan put City two-up before sub Grant McCann gave Scunthorpe hope with a late goal.
Coventry completely dominated the first half but failed to take a series of chances to open the scoring.
Both teams had started slowly, but when Aron Gunnarsson fired a volley goalwards in the 14th minute it brought Coventry and the crowd to life.
Clinton Morrison shot over from Stead's knock-back in the 19th minute as the pair showed a good understanding on Stead's home debut for the Sky Blues.
Chris Coleman's team were playing some good football and Carl Baker and Gunnarsson were particularly impressive in midfield.
Clingan had a free-kick saved by Joe Murphy in the 22nd minute before Martyn Woolford headed wide at the other end with one of Scunthorpe's few chances.
City produced one of the best passing moves of the game a minute later as Baker, Michael McIndoe and Stead combined to set up Clingan who cracked his shot wide.
Gary Hooper got a sight of goal in the 27th minute but his effort was blocked by defender Martin Cranie.
It seemed like only a matter of time before the home team would score as Gunnarsson saw another long-range shot tipped over by Murphy before Baker went on a mazy run before shooting just wide of the post.
After all their first-half dominance, Coventry could have gone behind but Hooper's back header was clutched in the air by Westwood.
The home side finally took the lead in the 55th minute when Stead received a pass from Baker and fired low past Murphy.
But Scunthorpe had a great chance to draw level five minutes later when Barnett gave away a penalty for a foul on Hooper and was sent off for his second booking.
Hooper appeared to hit a good penalty but Westwood made an outstanding save and Paul Hayes shot wide with the rebound.
The ten men of Coventry doubled their advantage in the 68th minute when Clingan hit a sweet free-kick past Murphy and then almost made it three when he shot from distance but this time the keeper saved.
McCann made it a shaky last few minutes for the home side when he scored with a shot on the turn in the 82nd minute.