Paul Hall had given Chesterfield a 20th minute lead at Saltergate, but Swindon showed character to come back, although their equaliser was controversial.
Referee Gary Lewis decided that a fierce shot from Hameur Bouazza had struck Steve Blatherwick on the hand, although a video later suggested it had hit the centre-half in the face.
Bouazza coolly sent Barry Roche the wrong way with the spot kick and that was enough to take Swindon's impressive run under manager Iffy Onuora to one defeat in 11 games.
Although the penalty decision was harsh the result was about right after Swindon displayed resilience and grit against a team just outside the play-off places.
Clear chances were few and far between on a bitterly cold night, although the pitch stood up well in the freezing conditions.
The pace of Chesterfield's front line always posed problems, although it was a long throw that unhinged the visitors' defence.
The ball was headed on and Hall was the first to react to steer a low right-foot shot past Rhys Evans from 12 yards.
Swindon responded positively with Andy Gurney curling a free-kick onto the roof of the net while Ricky Shakes should have done better in the 31st minute when Rory Fallon set him up.
Fallon's pass put Shakes in on the right but he lost his footing at the crucial moment and the ball was scrambled behind for a new corner.
Chesterfield moved up a gear at the start of the second half and forced a string of corners but Swindon survived and got their reward when Bouazza converted the 63rd minute penalty.
Chesterfield looked more likely to win the game after that but there were few genuine chances for either side in the closing stages.
Both managers made substitutions but the closest either side came to another goal was in injury time when Swindon survived a goal line scramble after Evans appeared to be fouled.
Swindon can take heart from the way they recovered while Chesterfield remain unbeaten in the League since late October.