Riyad Mahrez set up Jamie Vardy to score the winning goal on his return to the stating XI as Claude Puel's men booked their spot in the sixth round of the FA Cup.
The away side had their moments in the first half but rarely troubled the Leicester goal while they had goalkeeper Jamal Blackman to thank that the sides went into the break on equal terms.
He made a couple of superb saves to deny first Wilfred Ndidi's long-ranged effort and then Vardy from close. However, there was nothing he could do about Vardy's looping header in the 66th minute.