Walsall claimed a victory that seemed impossible after Stockport had dominated the majority of the game.
And even after Rhys Weston had given Walsall a 64th-minute lead, the visitors still should have taken advantage when Walsall striker Michael Ricketts was shown his second red card of the season for two bookable offences.
Walsall were also indebted to goalkeeper Clayton Ince for some magnificent saves.
Stockport, beaten only once in their previous ten away matches, looked lively from the start and winger Anthony Pilkington produced a good 17th-minute save from Ince with a low shot from 25 yards.
It was Pilkington again who had a chance in the 24th minute from a cross by James Tunnicliffe but he failed to connect cleanly with the ball.
Two minutes later young full-back Netan Sansara replaced midfielder Mark Bradley and immediately had an impact with a fine cross from which Ricketts headed over.
Stockport appealed for a penalty when on-loan striker Craig Davies went down in the box after 36 minutes and, although playing neat football throughout, the Hatters failed to create sufficient chances.
Two minutes after the interval it was Walsall's turn to appeal for a penalty when Jabo Ibehre went down under a challenge by Jim McNulty but referee Jon Moss thought otherwise.
Ince made a tremendous save in the 57th minute when Johnny Mullins set up Dominic Blizzard for a powerful shot which the big keeper dived low to turn past a post.
In the 62nd minute, with Walsall beginning to show a lot more spirit, Sansara had a sensational 40-yard shot pushed over the bar by Stockport keeper Owain Fon Williams.
The Saddlers were rewarded for their fight in the 64th minute when Weston scored with a fine header from a superbly taken corner by Chris Palmer.
But when Ricketts was given his marching orders three minutes later it looked likely that the visitors would get at least a point.
Ince however had other ideas and he made wonderful saves from a long-range Pilkington shot in the 71st minute and another from the same player with six minutes left.
As the match moved into stoppage time, Ince kept out another effort from Tunnicliffe, but at the other end Ibehre had a chance only to shoot into the side-netting.
