Peterborough almost gifted the hosts the lead towards the end of the first half when Shaun Brisley lost the ball to Jamie Vardy inside his own half. The Leicester new boy broke into the box before trying to square it to Jermaine Beckford. Gabriel Zakuani got there first, but was only prevented from scoring an own goal by a fine reaction save from Robert Olejnik.
The Foxes almost doubled their lead with 15 minutes left when Vardy tried to lob Olejnik, but the visiting goalkeeper did well to get back in time.
Just minutes later, however, the hosts did extend their lead. Vardy battled his way down the left before putting the ball into the box, finding Andy King who lashed his effort into the top corner.
Peterborough next match comes at home to Millwall on Tuesday, while Leicester face a trip to Charlton Athletic on the same day.