City were on the offensive from the off, with Alton Thelwell rescuing Orient early on when he managed to cut out Matty Oakley's cross to the far post where Matt Fryatt was ready to pounce.
But there was no stopping City on nine minute when Fryatt found Oakley, who beat Glenn Morris with an angled drive from ten yards.
The home side continued to excel and almost doubled their advantage midway through the first half when Steven Howard failed by a whisker to connect with Lloyd Dyer's cross.
Morris then saved superbly when he dived low to his left to keep out a 20-yard free-kick from Andy King.
The Foxes got the second goal their sparkling play deserved on 36 minutes when Oakley crossed and Howard outmuscled the keeper to set up Mark Davies, who headed home from five yards.
With a two-goal deficit to pull back Orient began to push forward after the restart, but struggled to make an impression on City's sturdy rearguard.
But the Londoners chiselled out a chance on 64 minutes when Charlie Daniels got in a good cross from the left, but Sam Parkin was unable to produce a firm enough header to trouble the keeper.
Further chances came with Dean Morgan's sliced shot well off target and a Jason Demetriou drive which drifted wide.
City hit back with a shot from substitute Paul Dickov which Tamika Mkandawire cleared off the line.
But Leicester put the result beyond doubt with an 84th minute penalty awarded after Davies had been felled inside the area by Mkandawire. Dickov stepped up to place the spot-kick low to the keeper's left.
Then Howard drilled the ball just wide when he got on the end of a Leicester move which involved 17 passes.
And deep in injury time Oakley preserved a clean sheet for Leicester when he cleared a Thelwell header off the line.