Although Rovers re-grouped and fought their way back into the game after the break, Posh never looked like losing their grip and a fourth goal late on was no more than they deserved.
Posh battered the Rovers goal from the off, and it took a superb one-handed save by Steve Phillips to keep out a fierce fourth-minute drive from last season's top marksman Danny Crow. But Phillips, making his Rovers debut after crossing the Bristol divide from City, was helpless when 20-year-old Jamie Day opened the scoring with a left foot 25-yarder after 10 minutes.
With Rovers penned in their own penalty area, Guy Branston sent a diving header wide before Richard Butcher, a summer capture from Oldham, opened his Posh account after 32 minutes with a jinking run past two defenders before placing a low right-foot shot wide of Phillips.
Chris Plummer provided a swerving cross from the right for Simon Yeo, who followed new Posh boss Alexander from Lincoln City, to bundle in the home side's third 10 minutes before the break.
Rovers had their chances, but Junior Agogo was strangely out of touch, sending a header high over the bar when well positioned and then the man currently attracting interest from Southend wasted another good opening by blazing well wide. It was no surprise when Agogo was replaced by Lewis Haldane for the second half and Rovers boss Paul Trollope also sent on Andy Sandell for Stuart Campbell.
Sandell quickly made an impact, crossing low for Sammy Igoe to pull a goal back seven minutes after the break before the progress was halted as Posh 'keeper Mark Tyler made a crucial save to keep out a curling free-kick from Richard Walker.
Posh surged forward again and Lloyd Opara was perfectly placed to seize possession 20 yards out and beat Phillips with a left-foot drive.