Loan signings Stuart Fleetwood and Josh Payne both scored on their Cheltenham debuts but Michael Raynes' late leveller earned a draw for Stockport.
Fleetwood scored against the run of play after 32 minutes, coolly sliding a shot past keeper Owain fon Williams.
County hauled themselves level 10 minutes into the second half with a brave diving header by Peter Thompson.
Payne slotted home after Williams parried Scott Murray's penalty, but Raynes headed home in the last minute.
Cheltenham: Scott P Brown, Gallinagh, Townsend, Diallo, Jeremy Gill, Montrose (Ben Gill 61), Payne, Russell, Murray, Connor (Vincent 61), Fleetwood (Caines 85). Subs Not Used: Armstrong, Perry.
Booked: Townsend.
Goals: Fleetwood 32, Payne 66.
Stockport: fon Williams, McSweeney (Vincent 82), Mullins, Owen (Rose 67), McNulty, Raynes, Anthony Pilkington, Dicker, Gleeson (Baker 82), Turnbull, Thompson. Subs Not Used: Blizzard, Rigby.
Goals: Thompson 55, Raynes 90.
Att: 3,796
Ref: Oliver Langford
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