Max Clayton's first-half goal handed Crewe their first League One home win of the season at the expense of managerless, winless Coventry.
Clayton should have opened the scoring earlier than he did but he missed the ball completely with the goal gaping.
Carl Baker wasted City's best chance when he somehow headed over the bar after Kelvin Mellor failed to clear.
But Clayton did get the eventual winner when he tapped in following AJ Leitch-Smith's miscued shot.
VIEW FROM THE DRESSING ROOM
Coventry City caretaker manager Richard Shaw:
"We had enough chances to win the game. We need a bit more quality in the final third and more concentration.
"We're quite a quiet bunch and I told them that if they have any aspirations of doing well this year they've got to demand more from each other; it's nothing personal, they've just got to demand more from each other on the pitch.
"They are working really hard. In terms of fitness, we looked a bit jaded in the first half. We played two hours on Tuesday in a game that was frantic and full of pace, and I think that took its toll, especially in the first half, until I brought some fresh faces on."