Clive Platt's well-taken late strike secured a win for Colchester in Paul Lambert's first game in charge.
Stephen Gillespie missed a chance after just 10 seconds, but the U's went in front after 20 minutes when Platt crossed for Perkins to side-foot home.
But Leon McSweeney crossed for Matty McNeil - later stretchered off with a head injury - to nod home an equaliser.
But Platt pounced from close range after latching on to a neat flick from David Perkins to sink Stockport.
Stockport: Forster, McSweeney, McNulty, Fojut, Rowe, Baker, Dicker (Johnson 90), Raynes (Turnbull 29), Gleeson, Thompson, McNeil (Anthony Pilkington 49). Subs Not Used: fon Williams, Kane.
Goals: McNeil 42.
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Booked: Hammond, Reid, Jackson, Wordsworth.
Goals: Perkins 20, Platt 87.
Att: 6,025
Ref: Darren Deadman (Cambridgeshire).
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