With a freescoring forward line you might expect Peterborough to be flamboyant, but they produced a performance full of defensive organisation and sheer hard work, while in contrast Rochdale looked sluggish and devoid of ideas.
Peterborough bossed the first half without really creating any clear-cut opportunities, but after the break they stepped up a gear and were good value for the win.
The opening goal came on 57 minutes with a well struck 25-yard drive by George Boyd which Rochdale keeper Sam Russell should have kept out.
A double substitution for the home side almost paid immediate dividends as one of them, Adam Rundle, crossed and found the other, Ben Muirhead, but he missed the target from less than six yards out.
The visitors doubled their lead and wrapped up the points on 76 minutes when the Rochdale defence failed to clear following a quick free-kick.
Boyd popped the ball back into the box and Aaron McLean greedily accepted the chance from 12 yards.