North End, conquerors of Crystal Palace in the Capital One Cup on Tuesday night, had only scored once in the league before the visit of Paolo Di Canio's team.
However, strikes from Akpo Sodje, Wroe and deadline-day signing Stuart Beavon had trebled that tally by half-time. Raffaele De Vita hit back for Swindon but John Welsh opened his Preston account to make sure of the points.
Sodje volleyed home after five minutes from goalkeeper Wes Foderingham's blocked clearance. Wroe then diverted Scott Laird's low cross into the far corner to make it 2-0 after 10 minutes.
Di Canio had seen enough and hauled off Foderingham after just 20 minutes, with the goalkeeper storming straight down the tunnel after a heated exchange with his manager. In Foderingham's place came 18-year-old debutant Leigh Bedwell.
The change made little difference and Beavon marked becoming Preston's 17th debutant this season by tapping in just before half time.
De Vita's drilled shot pulled one back for Town after 58 minutes but any hopes of a comeback were extinguished when Welsh smashed in his first Preston goal 20 minutes from time.