Hasney Aljofree's 88th-minute equaliser for Swindon left Gillingham on the brink of relegation to League Two.
The home side made a dream start, with Garry Richards heading in Nicky Southall's free-kick from the right.
Gillingham missed chances to snatch a second before Jon-Paul McGovern's corner was flicked on by Sean Morrison for Aljofree head home.
It means the Gills are almost certain go down if Cheltenham manage to pick up a point in their remaining game.
Gillingham: Stillie, Richards, Cullip, King, Southall, Crofts, Maher, Lewis (Ba 90), Nutter, Mulligan (Oli 67), Jackson.Subs Not Used: Kiely, Bentley, Griffiths.
Booked: Cullip.
Goals: Richards 2.
Swindon: Brezovan, Jack Smith (Joyce 86), Ifil (Morrison 34), Aljofree, Vincent, McGovern, Easton, Timlin, McNamee (Paynter 68), Cox, Peacock.
Subs Not Used: Phil Smith, Allen.
Booked: Peacock, Cox.
Goals: Aljofree 88.
Att: 6,334
Ref: Stuart Attwell (Warwickshire).
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