A goal in each half from Tommy Rowe and Britt Assombalonga handed Darren Ferguson's men another three points towards their quest to seal the fourth play-off spot.
Peterborough's recent inconsistency had given the chasing pack in League One hopes of leapfrogging them in the table.
Yet there were few signs of any Wembley hangovers as the hosts dominated the match against their East Anglia rivals.
Grant McCann almost gave the Posh the lead after 16 minutes but his left-foot snap-shot cannoned back off Sam Walker's post.
Then defender Shaun Brisley, who scored his first goal for Peterborough against Chesterfield on Sunday, was denied a second when Tosin Olufemi hacked his low shot off the line.
Posh captain Rowe finally broke the deadlock with a pinpoint header from a McCann corner after 26 minutes.
Assombalonga's clinical strike from 15 yards sealed the win after 65 minutes - hitting his 29th goal of the season.
Joe Dunne's men failed to get a shot on target as they slumped to a third straight loss and now sit just three points from safety.