World Cup winner Kante's scruffy 34th-minute volley and Jorginho's audacious penalty on the stroke of half-time put Chelsea in control before Pedro wrapped up the points in the closing stages.
Kepa Arrizabalaga, the world's most expensive goalkeeper, barely had a save to make on his Blues debut, while Jorginho slotted seamlessly into a well-balanced midfield, which refused to be out-hussled by David Wagner's Terriers.
Kepa, signed from Atheltic Bilbao for £72.1million on Thursday, had little to do for the opening 20 minutes as Chelsea hogged the ball, but made a hash of an early touch when he passed straight to Town midfielder Aaron Mooy.
Alex Pritchard fired Huddersfield's first effort straight at Kepa soon after, which the Spaniard comfortably dealt with.
At the other end, Huddersfield's debutant goalkeeper Ben Hamer, signed on a free transfer from Leicester, made a nervous start, twice putting the home side under pressure with misplaced passes from his penalty area.
Huddersfield enjoyed more possession towards the half-hour mark as Steve Mounie's rising effort cleared the crossbar and a series of crosses from Town left-back Chris Lowe tested Chelsea's defence.
But Chelsea took the lead in the 34th-minute. Willian's delivery from the left evaded Huddersfield's cover and Kante's mistimed volley span into the ground and inside the far post.
Huddersfield's response was swift, with Mounie heading Mooy's 36th-minute corner against the inside of the far post.
But the Terriers were dealt a hammer blow in the 44th minute when referee Chris Kavanagh awarded the visitors a controversial penalty.
Christopher Schindler's sliding challenge on Marcos Alonso was deemed illegal by Kavanagh and Jorginho craftily waited for Hamer to commit before clipping his spot kick into the opposite corner.
Huddersfield fans will have felt the half-time score was harsh, but Chelsea set about extending their lead after the restart.
Antonio Rudiger's header from Willian's corner was well saved by Hamer, low down to his left, and Alonso's acrobatic volley from another set-piece soon after clipped the crossbar.
Referee Kavanagh further incensed Town fans when failing to see Kepa had clearly pushed Philip Billing's 73rd-minute header over the target when awarding a goalkick instead of a corner.
Sarri sent on Eden Hazard for Willian with 14 minutes left and the Belgian helped put the game to bed.
Hazard sliced through Huddersfield's defence down the middle before setting up Pedro, who drove home a low angled shot into the bottom corner.
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