David Nugent stepped up and fired into the top corner, leaving Stephen Henderson between the visitors' sticks with no chance.
The striker doubled the hosts' advantage on 18 minutes when he bundled the ball in from close range after Martin Waghorn's rebounded strike fell invitingly for him.
Waghorn turned provider once again for Leicester's third, supplying a pass from the left for Lloyd Dyer to fire home from 12 yards and make it 3-0.
Both Waghorn and Dyer were involved in the hosts' next goal, playing a neat one-two before the latter crossed for Antony Knockaert to smash in and make it 4-0.
All that was missing from Waghorn's performance was a goal, and he put that right early in the second half when he rifled Andy King's pass into the top corner for Leicester's fifth.
Ipswich almost had a consolation goal on 71 minutes when Jay Emmanuel-Thomas got in behind the home defence and let fly, only to be denied by Stephen Henderson.
The rout was completed eight minutes from time. Marko Futacs drilled into the bottom corner following good work from Dyer to make it 6-0 to the Foxes at full-time.