Adam Doyle's late header earned Woking three points and condemned Stockport to a fourth straight league defeat.
Doyle headed in Billy Knott's cross with five minutes remaining.
Earlier, Woking's Brett Williams hit the crossbar from 25 yards inside the first two minutes, and shot wide from six yards later in the first half.
The Hatters rarely threatened the home side's goal and drop into the bottom six of the Blue Square Bet Premier with defeat at Kingfield.
VIEW FROM THE DRESSING ROOM
Woking manager Garry Hill told BBC Surrey:
"Winning our last two games and keeping two clean sheets is pleasing and the six points mean a lot.
"Adam Doyle has been absolutely different class in both games and his leadership along the backline and showed the players a lot of character.
"To go and get two clean sheets and win 2-0 and 1-0 has shown a great reaction and all credit to the players."