The hosts started brightly on a bitter evening. Johnny Mullins saw a looping header saved by Danny Coyne, then Gary Dicker nodded Anthony Pilkington's corner-kick just over the crossbar.
At the other end Steve Jennings was denied by a super save from Stockport 'keeper Fraser Forster.
Pilkington drove in a low shot which fizzed narrowly wide as it was Stockport who were on top in the opening quarter.
The next chance didn't materialise until the 44th minute though, and it went to Stockport. Stephen Gleeson headed into Paul Turnbull's path, but he smashed a shot well over the bar from 20 yards.
Rovers came close three minutes after the restart when Mullins had to be alert to clear Bas Savage's close-range effort off the line, but Stockport hit back immediately with Peter Thompson volleying into the side-netting.
Either side of the 55-minute mark Gareth Edds twice went close with decent shots for Rovers, but still there was no breakthrough.
Stockport came mighty close on 59 minutes when Thompson saw his shot, following a great cross from Michael Rose, strike the crossbar.
After that Turnbull saw an acrobatic volley well saved by Coyne as it was the goalkeepers that came out on top.