The Foxes opened the scoring after 23 minutes when a cross from Robbie Neilson was fumbled by Posh goalkeeper Joe Lewis and Andy King guided the ball into the back of the net despite the best efforts of Kelvin Langmead.
Leicester doubled their advantage five minutes later as DJ Campbell raced clear and coolly slotted the ball past Lewis.
Langmead had a header ruled out for a foul on Michael Morrison before Dany N'Guessan added a third early in the second half.
Howard claimed his first with seven minutes left but moments later Posh pulled a goal back thanks to a terrific free-kick from Grant McCann which sailed into the top corner.
Then in stoppage time, the Foxes rounded off the scoring when Howard swept home from close range.