The Foxes, unable to qualify for the knockout stages heading into the fixture, wasted little time getting started, opening the scoring within seven minutes when Jake Evans converted an early penalty.
Evans soon turned provider for Reiss Khela to double City's advantage at Princes Park, before Riley Carr extended the advantage on the hour mark.
A late flurry saw Mirsad Ali add a fourth with five minutes to play, before Will Daniels rounded off the scoring in the final minute of normal time.
Leicester remain fourth in the group after picking up our first points in PL Cup Group C, and conclude the group stage on Friday when Preston North End are the visitors to LCFC Training Ground (7pm GMT kick-off).
The details
Goals: Evans 7' (pen), Khela 16', Carr 61', Ali 85', Daniels 89'.