Both sides stuck to their football through a first half punctuated by two downpours and a hail storm, but clear-cut chances were few and far between.
County started well and forced early corners where Liam Dickinson saw a strong header nodded off the Posh goalline by Jamie Day.
County's John Ruddy then became the busier goalkeeper after dropping on Aaron McLean's effort from a Dean Keates corner before getting both hands to a header from Chris Westwood, who soared to reach a Day corner.
In between, County were stretched by a right-wing break from Adam Newton and, with the ball only partially cleared, home skipper Micah Hyde fed McLean who saw his shot superbly blocked by visiting skipper Gareth Owen.
Stockport wasted a great opening three minutes into the second period after substitute Anthony Pilkington, who had just replaced Michael Raynes, charged down a Westwood clearance.
Pilkington's crossed only tamely and Jason Taylor sliced his shot wide as the ball ran away.
Referee Michael Oliver booked three players - Posh's McLean and County pair Jason Taylor and Dickinson - following a 51st minute flare-up and seven minutes later the highly-rated Rowe was the coolest player on the park when putting County in front with a left-footed shot from 15 yards.
Chris Whelpdale headed against the crossbar as Posh tried to hit back and his replacement, Charlie Lee, also rattled the woodwork although Darren Ferguson's men were surprisingly short of ideas as they tried save a 17-match unbeaten record.
It could have been worse for Posh with Dickinson squandering the easiest of chances to double Stockport's lead in added time.