Jonny Howson scored in the ninth minute to secure a ninth successive home win for Leeds in their bid for promotion.
Stockport goalkeeper Conrad Logan, on loan from Leicester, stayed on his line as Jonathan Douglas's cross was stabbed home by Howson.
On-loan Leeds striker Liam Dickinson should have scored against his old club but shot against the crossbar.
Substitute Andy Robinson hit the bar for Leeds late on as they consigned County to a fifth game without a goal.
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Leeds:
Ankergren, Douglas, Marques, Naylor, Parker, Snodgrass, Howson, Kilkenny, Delph, Dickinson (Grella 86), Becchio (Robinson 54).
Subs Not Used: Lucas, Michalik, Hughes.
Booked: Marques, Delph.
Goals: Howson 9.
Stockport: Logan, Tunnicliffe (Halls 19), Josh Thompson, Raynes, Rose, Turnbull (Daniel Rowe 60), Tansey (Johnson 46), Vincent, Blizzard, Tommy Rowe, O'Grady.
Subs Not Used: Mainwaring, Pilkington.
Booked: Halls.
Att: 24,967
Ref: Phil Crossley (Kent).
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