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.
Vaughan, a constant menace up front, had other chances. Allsop brilliantly tipped over his volley from Hammill's ball over the top on 30 minutes.
He then fired just wide seconds after the re-start when he pounced on Oliver Norwood's long punt ahead of a sleepy Cherries defence.
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.
The visitors, hammered 6-1 by Watford on their last trip, have now conceded 11 goals in their last two away matches.
But the Cherries, perhaps guilty of being too open at times, caused Huddersfield problems down both flanks.
Simon Francis crossed from the right only for Harry Arter to head over from close range when unmarked early on.
Arter scored the only goal at the John Smith's Stadium when the teams last met as League One sides in December 2011.
Winger Ryan Fraser crossed from the left for Brett Pittman's overhead kick on 18 minutes.
The goal-bound effort was blocked by Town skipper Peter Clarke.
Pitman then worked an opening for Lewis Grabban, who saw his low shot turned round the post for a corner by home keeper Alex Smithies.
Bournemouth, in the second tier for the first time in 23 years, played attractive attacking football throughout.
Their reward came on 68 minutes when Francis crossed from the right and substitute Marc Pugh plundered a close-range consolation.
Bournemouth's afternoon was summed up when substitute Eunan O'Kane had to go off injured just 15 minutes after coming on.
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.