Late goals from Fabian Delph and substitute Malcolm Christie secured Simon Grayson his first victory since taking over as Leeds manager.
Stockport were ahead on three minutes as Johnny Mullins followed up to net after Karl Baker's shot was blocked.
Leeds' Jermaine Beckford hit the bar with an overhead kick, before Luciano Becchio equalised from close range.
Delph pounced from long range after 73 minutes, then Christie smashed home a half-volley with four minutes to go.
Stockport: fon Williams, Mullins, Tunnicliffe, McNulty, Rose (McSweeney 25), Anthony Pilkington, Blizzard, Gleeson, Rowe, Davies (Thompson 78), Baker (Turnbull 77). Subs Not Used: Dicker, Taylor.
Goals: Mullins 3.
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Leeds: Ankergren, Richardson, Marques, Michalik, Sheehan, Hughes (Prutton 89), Douglas, Delph, Snodgrass (Howson 64), Beckford (Christie 64), Becchio. Subs Not Used: Lucas, Robinson.
Booked: Sheehan, Delph.
Goals: Becchio 19, Delph 73, Christie 86.
Att: 10,273
Ref: Richard Beeby (Northamptonshire).
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