City came away with all three points to make it four unbeaten games against Leamington this season.
Second half goals from Nick Wright and Graham Hutchison sealed the win.
With City still revelling in FA Cup glory after the famous 2-1 win at The Ricoh Arena v Coventry City in the previous game, it was always going to be a tough game, but a good spell in the space of a few second half minutes was enough to ensure the win.
The first half was a fairly even encounter with both teams clearing off the line. Jordan Goddard's Corner was met by Stefan Moore and his goal bound header was cleared off the line by the head of Graham Hutchison.
With chances few and far between City introduced Jordan Murphy and Connor Gater in place of Mike Symons and Danny Jackman on 64 minutes then on 72 minutes Tristan Dunkley replaced Daniel Nti in a bid to break the deadlock.
It took just four minutes from Dunkley being introduced for City to take the lead. City won a corner which was taken by Ellis Deeney & it was Nick Wright who rose highest to head home to make it 1-0.
Five minutes later, City won a deep free kick & a well rehearsed move saw Sean Geddes cross for Graham Hutchison to prod home from close range to make it 2-0.
Leamington made late changes with Lee Moore and Aron Wint join joining the game and it took just a couple of minutes for them to pull one back. Morleys deep free kick to the back post was met by Danny Newton, who made no mistake from close range.
City survived three minutes of injury time, to seal another three points in a Vanarama Conference North League match.