Second-half strikes from Holly Findlay and Olivia Smart were enough to secure the victory for the Whites in only their fourth competitive fixture of the season.
Leeds started brightly in the first half with Molly Havard causing problems for the Stockport defence down the left side.
In the third minute she evaded two tackles before smashing the ball across the face of goal, but Laura Bartup couldn’t quite get on to it at the back post.
Stockport quickly gained control of the game though and went on to dominate the first half.
Lauren Davies came close for the hosts with a long-range strike on 37 minutes, before Maria Figueiredo forced Leeds goalkeeper Kirsty Johnson into a fine double save two minutes later.
Neither side could find the breakthrough before half-time though.
Leeds started the second half on top and were awarded a penalty on 55 minutes when the ball struck the hand of Levi Chambers-Cook.
Bartup stepped up but saw her effort saved brilliantly by Jess Linford.
The visitors didn’t let that affect them and broke the deadlock five minutes later through a stunning half-volley from Findlay.
The ball broke on the edge of the box and Findlay lashed it into the top corner.
Leeds made it 2-0 on 78 minutes. Olivia Smart’s free-kick from the left touchline sailed over Linford and into the back of the net.
Abbie Brown came close to making it 3-0 with a powerful shot from the edge of the box, but it whistled just wide of the post.