The Argentina striker converted in each half, either side of a double from Eden Hazard, to cap an impressive home debut for the club he joined on loan from Juventus last month.
Chelsea completed the rout in the 86th minute, when David Luiz's header got the better of Jonas Lossl with a hefty deflection off Elias Kachunga.
Maurizio Sarri's side were thrashed 4-0 by Bournemouth on Wednesday, leading to a post-match dressing-room inquest led by the head coach, but they rarely looked in trouble against a Huddersfield side who are 13 points adrift of safety at the foot of the table.
Higuain had come close with a half-volley before opening his Chelsea account 16 minutes in, running onto N'Golo Kante's clever pass and firing high past Lossl.
The Huddersfield goalkeeper had to parry a good strike from Cesar Azpilicueta as Chelsea began to dominate, with David Luiz wasting a great chance with a wayward header.
The visitors were growing into the game when Azpilicueta went to ground under minimal contact from Kachunga, allowing Hazard to send Lossl the wrong way from the spot and make it 2-0 before the interval.
Hazard continued to cause unease for the Huddersfield defence and he eventually struck the killer third goal, gathering Ross Barkley's pass, waltzing around Lossl and finishing left-footed.
Higuain made certain of both the victory and a memorable first outing at the Bridge three minutes later, sending a thumping effort off Terence Kongolo and beyond Lossl from the edge of the box after being set up by Kante.
David Luiz's header was diverted past his own keeper by Kachunga to compound a rotten outing for Huddersfield, who have earned just one league point since the start of December.
Chelsea back in the top four
Saturday's win lifts Chelsea above Arsenal and into fourth place, with the Gunners playing their game in hand away to champions Manchester City on Sunday.
The victory also means Sarri's side now have a goal difference five better than Arsenal's and nine superior to Manchester United's, which could prove important in the race for the Champions League places.
Huddersfield stay bottom with 11 points from 25 games and have now lost 11 of their last 12 league matches. Their chances of survival are looking slim.
Hazard a roaming nuisance
Although starting wide on the left, Hazard drifted across the Chelsea attack to his heart's content and wreaked havoc in the Huddersfield defence. The penalty decision was debatable, but he deserved his goals.
