Second-half goals from Nick Chadwick and Michael Paton saw off Bath City as Stockport recorded their first away win in the Blue Square Bet Premier.
Lee Phillips and Sean Canham both went close for City before the break but were unable to find a way past the impressive Matthew Glennon.
The Stockport keeper then kept out a long-range effort from Phillips before Chadwick turned in Paton's cross.
Paton then smashed home a ferocious 25-yard strike in stoppage time.
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Bath City manager Adie Britton told BBC Somerset:
"The first half overall, I was very pleased with the performance - that was our time in the game to go and win it.
"Unfortunately we missed the opportunities and we conceded at a time when we were well on top.
"On the night I think it was a little bit undeserved but there's been too many of them this season and no excuses can be made."