Paynter, a late summer arrival from Southend, capitalised on some woeful Bournemouth defending to net his first goals in a Swindon shirt.
His first came just three minutes after the break as a long ball up field from goalkeeper Phil Smith looked harmless enough.
A communication breakdown between defender Paul Telfer and goalkeeper Asmir Begovic saw the big Canadian shotstopper aim his clearance straight at Paynter, leaving him with the easiest of tap-ins.
He added a second on 64 minutes as another long ball by Smith caused havoc once more.
Paynter shrugged off his marker before setting himself and delivering a clinical right-foot finish off the near post and past Begovic.
His treble was complete five minutes from time as the lively Simon Cox broke down the left-hand side and crossed for Paynter to finish from just two yards.
Swindon started the game in similar emphatic fashion as Paynter and Cox both combined on six minutes for the on-loan Reading striker to score his first goal for the club.
The goal though seemed to spur Bournemouth into life and they enjoyed vast spells of possession in the first half with some notable passing moves.
Brett Pitman went close just before the half-hour mark but he couldn't quite stretch enough to connect with Darren Anderton's pass into the area.
The away side though were rewarded for their invention on 37 minutes as Danny Hollands drew them level.
The former Chelsea youth midfielder was at the end of a sequence of passes that could have graced the Premier League as Jason Pearce, Lee Bradbury and Jo Kuffour all combined to dissect the Swindon defence and release Hollands to finish in style.
Unfortunately for Bournemouth, that was as good as it got as the second half soon bore witness to the Billy Paynter show.