Vaughan then latched on to Martin Paterson's through ball five minutes later and coolly slotted past advancing Cherries keeper Ryan Allsop.
His hat-trick came from the spot on 58 minutes after Carroll was felled by Simon Francis. Vaughan confidently drilled the penalty into the roof of the net.
The B£600,000 summer buy from Norwich has now scored seven goals this season, including five in his last three league matches.
Town were already 1-0 up before Vaughan's first-half double thanks to a solo effort by livewire former Barnsley ace Hammill.
He showed good composure to jink past several Bournemouth defenders and then drilled a low shot in off the far post past Allsop.
Hammill, a summer buy from Wolves, became the first Huddersfield player other than Vaughan to score this season.
Bournemouth, in the second tier for the first time in 23 years, played attractive attacking football throughout and their reward came on 68 minutes when Simon Francis crossed from the right and substitute Marc Pugh plundered a close-range consolation.
Huddersfield had the last word though when Adam Clayton let rip from 25 yards on 78 minutes, his shot rocketing into the top left corner.