Gary Johnson's men overran Rovers with a second-half attacking onslaught launched by fans' favourite George Boyd.
He broke the deadlock when accepting a 57th-minute pass from defender Kelvin Langmead and drilling a low shot past Mikkel Andersen from 15 yards.
Only a fine goalline clearance from Wayne Brown prevented Langmead from doubling the lead with a bullet header, but Posh were soon back on the goal trail.
Aaron Mclean struck at the second attempt with 17 minutes remaining after dancing round Andersen and skipper Grant McCann added a polished finishing touch when tucking away a classy free-kick late on.
It was not all plain sailing for Posh as they were reliant on a couple of fine saves from goalkeeper Joe Lewis, blocking an effort from Will Hoskins just before the half-hour before he then pulled off an even better stop to thwart Jeff Hughes soon after.