Stockport and Tranmere put in plenty of work but failed to produce a goal on a bitterly cold night at Edgeley Park.
Johnny Mullins and Gary Dicker both went close for the home side with early headers before Rovers' Steve Jennings drew a fine save from Fraser Forster.
County had two late chances as Peter Thompson hit the bar and only a good Danny Coyne save denied Paul Turnbull.
Tranmere ended with 10 men after Andy Taylor was booked twice in quick succession in the dying minutes.
Stockport: Forster, McSweeney, McNulty, Mullins, Rose, Gleeson, Dicker (Taylor 66), Turnbull, Rowe (Baker 74), Anthony Pilkington, Thompson. Subs Not Used: fon Williams, Tunnicliffe, Kane.
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