Crawley took the lead in the 5th minute and although Andy Williams’s 20th goal of the season had brought Town level in the second half, Gavin Tomlin’s late thunderbolt gave the visitors all three points.
Mark Cooper made two changes with Ben Gladwin and John Swift starting in place of Raphael Rossi-Branco and Louis Thompson.
Crawley kicked off playing toward the Town End with light snow falling and had the better of the opening exchanges before Anthony Wordsworth scored from close range in the 5th minute after the ball had been crossed from the left wing.
Shortly afterwards Tomlin fouled Swift 6 yards outside the Crawley penalty area and Swift got up to take the free kick but his effort went narrowly wide of the near post.
Swindon enjoyed plenty of possession without finding any clear opportunity until the 20th minute when Kasim fired in a shot from outside the area which Crawley keeper Lewis Price saved easily.
Crawley responded with a header by Pogba which went well wide of the goal before Swindon launched another attack.
The visitors were looking more decisive in attack and had an opportunity in the 32nd minute through Gwion Edwards but his first time effort was always rising and went over the bar.
The first yellow card was shown to Nathan Thompson for tripping McLeod just inside the Town half but the resulting free kick was cleared.
Town had two corners which led to nothing and there was a yellow card in the 37th minute for Byrne for tripping a Crawley player near the halfway line.
Gavin Tomlin was shown a yellow card for several fouls in the 42nd minute after he had attempted to trip Byrne.
Andy Williams had an attempt on goal in the 45th minute but the keeper took the ball cleanly down to his right.
Town’s best chance in the two added minutes was a free kick in a central position 30 yards from goal but Kasim’s woeful effort flew well over the crossbar which was the cue for the half time whistle.
Louis Thompson replaced Toffolo at the start of the second half and Town started strongly leading to a corner and when that was taken, the ball fell to Kasim but his effort went wide.
Andy Williams was presented with a great chance in the 51st minute when he received a first time pass from Byrne but his shot struck the keeper and the ball was cleared.
McLeod was shown the yellow card for impeding a Town player at a goal kick in the 55th minute.
Swindon equalised in the 58th minute thanks to a smart move started by Jack Stephens who advanced down the right wing before sending a measured pass to Andy Williams inside the Crawley area and he flicked the ball past the goalkeeper for his 20th goal of the season.
Town continued to push forward in search of a second goal and went close through Ben Gladwin but his flicked header from a corner went narrowly wide of the goal.
Town were awarded a freekick just outside the penalty area for a foul on Stephens but the resulting cross evaded all the Town forwards and went out for a throw in.
Nathan Byrne sent in a superb cross from the right wing to the back post for Swift to head goalwards but the ball went wide of goal in the 72nd minute.
Town had another corner in the 75th minute which led to Turnbull heading over and three minutes later Gladwin’s curled effort was pushed away by the keeper.
Jermaine Hylton made his home debut in the 79th minute replacing Michael Smith.
Town were awarded a free kick in the 81st minute for a foul on Williams but Byrne’s cross was headed away by the defence.
Nathan Byrne was doing his best to carve out a chance for Town with some determined running down the right wing but no Town players could get on the end of his crosses.
Bobson Bawling replaced Pogba for the visitors in the 88th minute and disaster struck almost straightaway when Tomlin outmuscled the Town defence from a long ball forward and he fired in a powerful shot to give his team the lead.
McLeod and Tomlin were replaced by Matt Harrold and Jimmy Smith as Crawley manager Dean Saunders tried to hang onto his team’s lead.
Richard Wood was shown a yellow card in added time for fouling Turnbull who was also cautioned for his reaction but there were no late chances for the Robins to get back in the match.
The final whistle was blown to end a disappointing match for Town against Crawley who had started the day in the bottom four in League One.