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The visitors almost took the lead against the run of play as Morten Gamst Pederson blasted a shot at goal but Kaspar Schmeichel managed to tip the ball over the bar.
Leicester should have gone ahead in the 27th minute but Michael Keane somehow missed from six yards out after he followed up on the ball after Chris Wood's overhead kick was blocked on the line.
This miss wasn't costly as Nigel Pearson's side went ahead through Wood as he headed past Jake Kean after Ben Marshall found the striker down the right.
The Foxes doubled their lead before half time as Harry Kane found the net as he headed the ball home with Marshall again the provider.
Leicester almost put the game out of sight when Lloyd Dyer picked up the ball outside the area and fired a vicious shot at goal but Kean made a good stop.
The home side made sure of the points as Andy King headed the ball in from close range from Martyn Waghorn's good delivery from a corner.