New signing Luke Rooney gave Swindon the lead in the 39th minute with his first goal since arriving from Gillingham last month and Paolo Di Canio's team never looked back.
Swindon goalkeeper Wes Foderingham made outstanding saves from Tyrone Barnett and Kyle McFadzean as Crawley went in search of an equaliser.
But Swindon underlined their superiority in the second half with goals from Billy Bodin and Paul Benson.
Bodin made it 2-0 in the 53rd minute with a fierce shot from the edge of the area after Paul Caddis had set him up.
Benson made certain of an emphatic win, Swindon's 17th in the league this season, when he finished off a sweeping move involving Allan McCormack and Bodin.
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