The first chance fell to Stockport on nine minutes. Dominic Blizzard headed the ball into Jason Taylor's path, but he couldn't quite turn the ball home from close range.
Liam Dickinson volleyed wide from distance, then Anthony Pilkington tried an ambitious overhead kick which flew harmlessly wide.
Stockport were well on top early on and Pilkington saw a shot blocked, before City keeper Scott Loach produced a superb point-blank save from Tommy Rowe on 24 minutes.
The pressure still mounted on Stuart McCall's Bradford and Blizzard was next to go close as he headed just over from eight yards.
City finally went close to a goal after 36 minutes. Taylor's clearing header only found Paul Evans and he flashed a super volley inches wide of John Ruddy's post.
It was soon back to the other end though and City's Darren Williams came to the rescue as he desperately cleared Blizzard's close-range shot off the line.
Perhaps inevitably, it was Bradford who went into the lead seven minutes after the restart. The on-rushing Joe Colbeck was checked by Stockport keeper Ruddy in the box and up stepped Peter Thorne to coolly slot home the spot-kick.
The hosts were stunned, but they finally got their deserved goal on 69 minutes when Shaleum Logan crossed and Pilkington drove home a low angled shot from 15 yards.
Nine minutes later the hosts went in front, when impressive left-back Michael Rose curled home a cracking 20-yard free-kick following a foul on Taylor.
David Wetherall headed inches wide for Bradford in stoppage time, but the Hatters held on for the victory.