Understandably nervous in the opening stages, Rochdale were indebted to keeper Matt Gilks as he did well to keep out headers from the eventual match winner Aaron McLean and Trevor Benjamin.
After surviving that nervous opening Rochdale grew in confidence and began to test a resolute Peterborough rear guard that has now kept nine clean sheets in 11 away fixtures.
French winger William Mocquet stung the hands of keeper Mark Tyler with a terrific drive from the edge of the penalty area, and skipper Gary Jones making his 300th appearance for the club was also denied from the edge of the box.
The Peterborough back four were by now working overtime with several last ditch blocks, but were fortunate not to concede a penalty just before the break when Rochdale's leading scorer Chris Dagnall appeared to be pulled down in the box.
Early in the second half the best move of the game saw Dagnall released into the box but his hard low drive was again very well saved by Tyler.
Against the run of play, the visitors took the lead when McLean turned sharply in the box and rifled a low drive between keeper Gilks and his near post.
Parkin threw on substitute Adam Rundle and Morike Sako but despite frantic late efforts and a further appeal for a penalty they were unable to claw themselves back into a game that they certainly did not deserve to lose.