Simon Moore gave the hosts a lead in the opening minute which they held at the break, before Coventry’s strength gave them a 3-1 win.
After Moore’s goal, Jack Lane headed wide from a corner.
The whole of the ground thought it was two soon after Dan Meredith played Devon Kelly-Evans through one-on-one with Moore and Kelly-Evans slotted the ball under the Sky Blues custodian but Jack Burroughs did superbly to clear the ball off the line.
The trend of the half being all Leamington continued as Devon Kelly-Evans was once again making Simon Moore earn his keep, forcing him into a sharp save from an angle. Coventry fan Jack Edwards was the next to have a chance and his effort was cleared off the line.
Theo Streete made his first appearance for Leamington and was left with a late challenge from Tyler Walker that looked nasty, with Streete having to receive treatment.
Martyn Waghorn slid in what City fans thought was the equaliser but Waghorn was adjudged to be offside, which gave Leamington the lead at half time.
The Sky Blues named a completely different side in the second half, still first team players and their freshness told as they started the second half much better. Matty Godden was the danger as he started quickly, forcing Jake Weaver into another early save.
Leamington lived to regret their missed chances as Matty Godden equalised on the hour mark, guiding a close range header past Weaver.
Godden had a goal ruled out a couple of minutes later, but took his next chance legally as he made it two for the visitors. Jake Weaver kept the scores close as he made more saves.
Portuguese forward Fabio Tavares must have been reminded of his days at Curzon Ashton playing on National League North grounds, and he made it three with another close range header.
Simeon Maye was brought into the game late on - his first time back out since 2nd October 2021.