Coventry saw off Oldham to pick up their first league win of the season, and their first under Mark Robins.
Christian Montano's 20-yard drive was saved by visiting keeper Joe Murphy, and Jose Baxter and Matt Derbyshire had half chances for the hosts.
David McGoldrick missed a rare chance for the Sky Blues prior to the break, before Baxter thumped the post.
Derbyshire was twice denied by Murphy, before Cody McDonald headed in a winner at the death.
VIEW FROM THE DRESSING ROOM
Oldham Athletic manager Paul Dickov told BBC Radio Manchester:
"We're all frustrated. Like the previous three games, I'm talking about us being the better team, probably deserving to win the game and us getting nothing out of it.
"A little bit of luck didn't go our way, but when you're struggling a little bit, you have to make sure you defend properly.
"We switched off once. We didn't stop the cross or pick up the man in the box, and we conceded from it."
Sky Blues manager Mark Robins told BBC Coventry & Warwickshire:
"That was one of the worst games of football I have ever seen in my life. We couldn't pass the ball. We were awful. We gave the ball away. I can be hypercritical, but I'll take the three points because that breeds confidence. It wasn't a great game, but we'll take it.
"It was the reward the fans deserve for Wednesday night and the amazing support we had. They make great noise and it really is a help to us.
"We've been fortunate today because our play could have been punished and it hasn't been and thankfully we've got off the mark with our first win."