Craig Mackail-Smith's goal steered a nervous Peterborough one step closer to a second successive promotion.
The former Dagenham hitman collected an Aaron Mclean pass before chipping over advancing keeper Conrad Logan.
Posh dominated, George Boyd forcing Logan into a fine save five minutes before the break, Dominic Green rolling his follow-up against an upright.
Stockport almost levelled when Oli Johnson hit the crossbar following Leon McSweeney's free-kick.
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Peterborough: Lewis, Martin, Morgan, Westwood, Lee, Boyd, Keates, Coutts (Frecklington 87), Green (Whelpdale 59), Mclean, Mackail-Smith. Subs Not Used: McKeown, Batt, Blanchett.
Booked: Coutts, Boyd
Goals: Mackail-Smith 25
Stockport: Logan, Halls (Johnson 33), Raynes, Josh Thompson, Tommy Rowe, Vincent, Turnbull, Tansey (Daniel Rowe 45), McSweeney, O'Grady (Mainwaring 74), Peter Thompson. Subs Not Used: Rose, Roberts.
Booked: McSweeney, Turnbull
Att: 8,333
Ref: Lee Probert (Wiltshire)
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