Posh never looked comfortable against a Morecambe side that crowded five players into midfield although Josh Low managed to find space on the right early on.
However, after the former Leicester City man pulled a muscle and was replaced by George Boyd on 22 minutes, Posh lost their way and found it difficult to create any openings.
Boyd saw a cross snatched from the head of Chris Whelpdale by Joe Lewis and the towering Morecambe goalkeeper was equally commanding in the air dealing capably with centres from Jamie Day and Claude Gnapka.
Morecambe were rarely ambitious in attack although their lone striker Matthew Blinkhorn did chase Damien Allen's ball from midfield and force home keeper Mark Tyler to make a save at full stretch.
It took a penalty to break the deadlock, Aaron McLean beating Lewis from the spot on 63 minutes after Adam Yates caught Jamie Day with a late challenge.
With Posh finally looking more lively, Lewis went down at Danny Crow's feet to atone for an earlier mistake and then saved superbly as substitute Craig Mackail-Smith looked set to score with his first touch.
Morecambe were still asking questions at the other end and Tyler tipped over impressively after a Neil Sorvel shot took a deflection off home centre-back Craig Morgan.
Yet it was a slip by Tyler that let in Thompson with seven minutes left. The home man flapped at a cross by Morecambe danger-man Michael Twiss and the 26 year-old needed one touch before firing into the net through a crowded goalmouth.