Coventry manager Mark Robins praised his team's "winning qualities" after they condemned Tranmere to only their fifth defeat of the season.
The Sky Blues showed two sides to their game to overcome the League One leaders 1-0 at the Ricoh Arena.
They dominated Ronnie Moore's men in the opening period and should have had more to show for it than Leon Clarke's 19th-minute strike from close range. But Rovers came back at City in the second half and the hosts ended up hanging on.
Robins said of his team: "They showed winning qualities. I thought we played really well in the first half. We played less well in the second half.
"They changed their shape for the first time this season which was a compliment to us and we showed that they warranted doing that in the first half because I thought we passed it really well.
"We deserved the lead. All the stats were in our favour in the first half and in the second half I thought they edged it.
"We started to become a little bit sloppy and they caught us on the break and outnumbered us a couple of times and it took an inspired Joe Murphy to get us out of the mire and keep a clean sheet.
"The important thing was the three points and the players have come up trumps so I am delighted on two fronts."