Craig Morgan sliced into his own net on 6 mins, Matty Fryatt got on the scoresheet to make it 2 - 0 at half time.
Any hopes of a Posh comeback were dismissed with goals from Andy King on 70 mins from a header and Steve Howard in the 90th minute to make the victory more emphatic.
Leicester are now 4 points clear at the top of the table and look forward to a Boxing Day clash against managerless Leeds Utd at Elland Rd.