Silko Thomas' early goal settled the contest at Prenton Park as the young Foxes responded to Friday's 4-0 Premier League Cup defeat at Fulham in stunning fashion.
Having been beaten 7-1 by Sky Bet League 1 side Wigan Athletic on matchday one, the side coached by Ben Petty are up against it to qualify for the knockout stages of the competition, but did their chances no harm by dispatching fourth-tier Tranmere on their own patch.
At the scene of the First Team's Carabao Cup victory over the same side in late August, the visitors got off to the best possible start when a long ball forward was well kept in by Wanya Marçal before the winger cut it back for Thomas to finish - the midfielder atoning for his sending off against the Cottagers four days earlier.
That's how it stayed in Birkenhead, with City able to keep Rovers at bay and claim victory over senior opposition, moving onto three points in Northern Group D.
Leicester now sit third, one point behind both leaders Wigan and second-place Fleetwood Town - who they face in the final group fixture on 7 November (7pm GMT kick-off). A win over the Cod Army at Highbury Stadium would see the Foxes qualify.
The details
City: Young; Cover, Nelson (c), Wilson-Brown, Ali; Godsmark-Ford, Cartwright, Raikhy (Amartey 85'); Richards (Grist 87'), Marçal, Thomas (Pennant 67').
Subs not used: Doherty, Hill, Aluko, Neale.
Goal: Thomas 9'.
Images: Tranmere Rovers FC.