In a low key affair, supporters had to wait until the half-hour mark for the game's first serious assault on goal when an Andy King thunderbolt from 22 yards ricocheted off the bar with John Sullivan reacting quickly to block Matty Fryatt's follow-up shot.
Just before the break Leicester keeper David Martin was almost caught napping when he needed two attempts to smother a low drive from Nicky Forster.
Jack Hobbs came close to turning a Dean Cox cross into his own net in the 50th minute but Martin kept City level with an instinctive block.
Leicester upped the tempo as the game entered its final phase with King going close when his 22-yard shot was deflected onto a post.
Fryatt then squandered a glorious chance to win it for City deep into injury time when he blazed a Cleverley cross over the bar from eight yards.