Darren Ferguson's men extended their unbeaten League One run to nine matches as they saw off a Town side that has leaked nine goals in two games.
Aaron McLean marked his first start since dislocating an elbow at the beginning of September by opening and completing the scoring.
He set the ball rolling after 12 minutes when rifling into the roof of the net after a mesmerising George Boyd run.
Provider then became scorer when Posh added a second goal following a lightning 24th minute breakaway.
Boyd arrowed a left-foot finish past keeper Matt Glennon after being released by a Paul Coutts pass.
The alarm bells should have been ringing for Huddersfield after wideman Chris Whelpdale twice went close inside the opening six minutes.
He slid a glorious Boyd cross wide before seeing a scuffed shot from point-blank range kept out by the legs of Glennon.
Huddersfield had their moments as an attacking force with defender Nathan Clarke prodding a Robbie Williams cross wide early on and later only a well-timed Russell Martin tackle prevented the dangerous Gary Roberts from getting on the end of a an Ian Craney delivery.
But Town were under the cosh again as Posh doubled their lead in the second period.
Only ten minutes had passed when Whelpdale finally found the net with a back post header after being picked out by another cracking Boyd cross.
McLean then heaped further misery on Huddersfield boss Stan Ternent by adding a fourth goal with his final effort before substitution when a low drive went straight under Glennon's body.
There was more misery for Town when skipper Chris Lucketti was sent off in stoppage time for a professional foul.