The Magpies had led early in the second half, only to be hit by two late sucker-punches.
After an impeccably observed minute’s silence, the match started in a scrappy fashion with neither side getting a real foothold in the game.
Stockport were trying to play a long-ball game, but Chorley coped well.
The Magpies almost gained the lead after 25 minutes. A smart through ball from Laura Walker found Mel Ball, who rounded the goalkeeper, but the angle was tight and she fired into the side netting.
Katy Morris, who looked lively throughout, then tried her luck from 30 yards, but her effort flew wide.
Rebecca Kemp was having a lot of joy on the right, and her cross was almost turned in by Grace Vella.
Just before the half-time whistle, Stockport were awarded a free-kick on the edge of the box, which Rachel Darbyshire saved superbly to her right.
Chorley came out of the blocks quickly in the second half, and they took the lead shortly after the restart.
Megan Searson arrowed a ball into Kemp, who whipped in a dangerous cross which Ball headed home.
Chorley continued to dominate and Lisa Topping showed some lovely skill on the left but Ball could not quite connect with her cross.
Stockport had a chance to equalise on 60 minutes when striker Mapp had a free header, but Darbyshire pushed the ball to safety.
With just minutes to go, Stockport equalised as a long ball was thumped into the box and Chloe Mapp stabbed past Darbyshire.
And Stockport scored the winner with the last kick as Claire O’Reilly’s free-kick took a wicked deflection.