The home side started strongly and Callum Camps broke the deadlock in the 17th minute when a Donal McDermott pass was deflected fortuitously into his path.
The midfielder took full advantage, poking the ball past Posh goalkeeper Ben Alnwick from eight yards out.
Peterborough struggled to fire but grew into the contest after Dale defender Jim McNulty sliced Marcus Maddison’s cross inches over his own crossbar midway through the first half.
Both Jon Taylor and Joe Gormley tested home goalkeeper Josh Lillis before the interval but Dale were good value for their half-time lead.
Gormley shot across the face of goal and wide when well placed 15 minutes into the second half while Peter Vincenti’s header hit the foot of a post at the other end.
Dale netted their second goal in the 69th minute when Ian Henderson picked out substitute Reuben Noble-Lazarus who drilled a low shot across Alnwick and into the bottom corner of the net.
Henderson had a late shot saved while substitute Calvin Andrew had a couple of openings but saw one effort well saved by Alnwick while the other he blazed over the crossbar.