Chesterfield conceded a 77th minute goal to Yaser Kasim that means their relegation battle moves on to the Bury home game next week.
Kasim stroked in left-footed from just inside the box after a patient build-up down the right, the goal coming just after Jonathan Obika has spooned the ball over from three yards and Michael Doughty had hit the inside of the post.
Spireites played the last few minutes of the game with ten men after Charlie Raglan picked up a second yellow.
Danny Wilson made one change from the side that reached 50 points on Tuesday evening, Chris Herd replacing Jamal Campbell-Ryce, but the latter was soon in action, replacing Lee Novak who took a knock early on, battled on and forced a fine save from Jake Kean before succumbing to an injury that could bring his Spireites career, on-loan from Birmingham City, to an end.
Jay O'Shea also saw Kean tip over a fine shot but after the break, Chesterfield didn’t offer enough to threaten the win and after conceding, rarely looked like gleaning a point, so it’s a shaky afternoon against the Shakers and all eyes will be on Wigan at Blackpool for some extra insurance.
Swindon: Kean, Barry, Branco, N.Thompson, Turnbull, Brophy, Kasim, L.Thompson, Doughty, Obika, Ajose. Subs (not used): Henry, Sendles-White, Rodgers, Marshall, Iandolo, Hylton, Cooke.
Chesterfield: Lee, Raglan, Hird, Anderson, Talbot, Herd (Slew 66), Liddle, Banks, O’Shea, Ariyibi, Novak (Campbell-Ryce 25). Subs (not used): Chapman, Ebanks-Blake, Dimaio, Gardner, Humphreys.
Referee: Trevor Kettle (Rutland)
Bookings: Herd, Raglan (Chesterfield)
Sent-Off: Raglan (Chesterfield) Two yellows, 87 mins