Posh arrived at the Walkers Stadium confident of equalling a club record of 17 unbeaten League games, but it was City who earned all the plaudits with a sixth straight win.
The visitors started brightly enough testing City with a brace of early corners, but the first clear chance fell to Matty Fryatt who, after springing the offside trap, fired in a 12-yard shot which the keeper kept out with his legs.
But the Foxes took a sixth-minute lead when Fryatt chased a seemingly lost cause on the right before crossing into the penalty area where Peterborough defender Craig Morgan sliced the ball into his own net while attempting to clear.
City continued to press with Joe Lewis forced to beat away a fierce drive from Mark Davies before Steve Howard side-footed wide from 12 yards.
Peterborough came close to an equaliser on the half-hour mark when Aaron McLean struck a post from eight yards with Craig Mackail-Smith crashing the rebound against the bar before McLean blazed the loose ball into the crowd.
Lewis then did well to chest away Fryatt's close-range shot, but it was the Leicester striker who won his next dual with the keeper when, on 38 minutes, he latched on to a Jack Hobbs long ball and rounded the Posh defender before guiding home an angled shot from 12 yards.
The visitors went in search of a quick reply after the re-start with McLean shooting narrowly wide from 20 yards before firing straight at the keeper from a closer range.
When Leicester responded, Davies fizzed a 25-yard shot just wide before George Boyd went close for Peterborough when he turned and fired into the side-netting from 14 yards.
But City continued to pose a potent threat themselves with Andy King testing the keeper with a header from a Matt Oakley corner.
Chances continued to arrive at both ends with Charlie Lee glancing a header wide before Lloyd Dyer was denied by Boyd's last-ditch tackle.
But the visitors' defence buckled on 70 minutes when Oakley played in a free-kick to the near post with King ghosting in beyond a static defence to score with a firm header.
And Howard sealed the victory in the final minute when he took advantage of a back-pedalling defence to score with a well-struck drive from 22 yards.