New manager Chris Coleman now knows the size of his task to try and keep the Sky Blues in the Championship.
Scunthorpe too boosted their hopes of survival at this level with only their third win in 23 games.
The home side started brightly and might have had the lead in the early minutes when striker Ben May missed a good chance.
It was leading marksman Martin Paterson who did open the scoring for Scunthorpe in the 15th minute when he curled an excellent 25-yard shot past goalkeeper Andy Marshall for his 14th goal of the season.
But Coventry were back on level terms six minutes later when midfielder Kevin Thornton levelled from the penalty spot after he himself had been brought down by full-back Marcus Williams.
It was only the second goal in seven away games for City, who are struggling to find a cutting edge up front.
They did go close early in the second half when striker Leon Best flashed a shot across the face of the goal and just wide of the far post.
They had an escape when midfielder Jay Tabb cleared off the line from Ian Morris, and it was Scunthorpe who looked like they may snatch all three points.
Scunthorpe were magnificent at the back, with Izzy Iriekpen impressing at the heart of the defence. He swept up everything and kept Coventry danger man Michael Mifsud relatively quiet.
The winner came in the 66th minute when Jack Cork - the England Under-19 player on-loan from Chelsea, squeezed a shot past goalkeeper Marshall into the top corner from what seemed an impossible angle.
Cork could have added another in the closing stages but lifted his shot over the bar to leave Scunthorpe facing an anxious finish.