Tomlin strike sinks Swindon
Crawley, who fashioned only three shots in the entire game, had been hanging on after a 60th-minute equaliser by Andy Williams cancelled out an early strike by Anthony Wordsworth.
But they went on to claim their first away victory since mid-August and complete a remarkable double over Swindon, whose promotion prospects are faltering after a fourth defeat in five matches.
Crawley stunned Swindon with a cleverly worked sixth-minute opener by Ipswich loanee Anthony Wordsworth, created by Gwion Edwards.
Williams equalised on the hour from a measured pass by Jack Stephens, but Swindon were stunned two minutes from the end of normal time when Tomlin sent a rasping cross-shot into the far corner.