Darren Ferguson's men needed just 80 seconds to open the scoring and went on to claim their biggest win for three years. They could even afford to miss two penalties along the way.
Tommy Rowe was the player to deliver the perfect start, racing into the box to tuck away Craig Mackail-Smith's low cross from point-blank range. League One's top scorer Mackail-Smith went from provider to scorer as he doubled Posh's advantage with a high-class header after 24 minutes.
And the points were in the bag by the time George Boyd weaved his way through a couple of tame tackles and nonchalantly prodded the ball under the body of Carlisle goalkeeper Adam Collin in stoppage-time at the end of the first half.
Skipper Grant McCann spurned a glorious opportunity for number four when seeing his spot-kick - awarded for a Frank Simek shove on Mackail-Smith - saved by Collin early in the second period. Carlisle then had on-loan centre-back Liam Cooper dismissed for a second caution just after the hour and Posh mercilessly picked apart the 10 men in the final quarter of an hour.
Defender Ryan Bennett lashed in on the half-volley after 77 minutes before Boyd added the fifth with a deflected volley eight minutes later. Substitute David Ball brought up the half-dozen when slamming home after being picked out by fellow replacement Nat Mendez-Laing with a minute remaining, and there was still time for Boyd to miss a second Posh spot-kick in stoppage time to see his hopes of a hat-trick go begging.