Freddy Eastwood sealed the points for Coventry as Nottingham Forest missed out on the chance to make up ground at the Championship summit.
Eastwood prodded in a close-range rebound midway through the first half after Forest keeper Lee Camp had stopped a Richard Wood effort.
Joe Garner and Guy Moussi both headed narrowly wide as third-placed Forest dominated for long stretches.
Gary Deegan and Michael McIndoe both threatened for City late on.
Coventry manager Chris Coleman:
"Forest are one of the best teams in the league so it's a good result. We knew it would be a hard match but the lads were fantastic.
"Some of our defending was top notch and our strikers did well against a very strong defence.
"We said don't sit back and we didn't - but they pushed us back. We had one or two scary moments but we did well."
Nottingham Forest boss Billy Davies:
"We sit four points off the top of the league and are in a wonderful position with 16 games to go.
"We've got to appreciate the position we're in and look forward. I said to the players that this is an experience for them and they should enjoy it.
"They should be proud of where we are. They've given themselves a great chance and there will be no disappointments."
Took me completely by surprise this one! Didn't even realise there was a mid-week fixture?