But despite the margin of victory Sarri concedes the Chelsea players are still not playing at the level he wants them to be.
Alex Pritchard was a unsafe creative force in the final third, Steve Mounié came close on three occasions and hit the post with a close-range header just minutes after Kanté opened the scoring.
After a slow start to the game, which saw David Luiz playing long balls as opposed to passing through the midfield, Jorginho started to take control of his team-mates. After a choppy opening half hour, N'Golo Kante made the breakthrough and, from that point on, there was only going to be one outcome.
Sarri opted for a 4-5-1 formation, abandoning Conte's well-established system with three central defenders, and Chelsea struggled initially to get a foothold in the game.
Maurizio Sarri feels Chelsea will continue to improve under his stewardship, but the club's new coach will not aim to repeat his winning formula from Napoli.
A strike from World Cup victor N'Golo Kante, Jorginho's penalty on debut and a late goal for Pedro were enough to hand Maurizio Sarri a first win in the Premier League.
They started the match brightly and also debuted a new stopper, with Ben Hamer starting their first match ahead of Jonas Lossl following an impressive pre-season.
"In the first half we started on the front foot, where we really wanted to be active", he said.
Eyes were obviously on debutants Jorginho and Arrizabalaga and the pair gave excellent accounts of themselves, with the former scoring a cheeky penalty in the first half.
Then Jorginho, who made the move from Napoli with Sarri, converted a disputed penalty.
Kongolo initially joined the Terriers on loan for the second half of last season and performed well enough at the back for Huddersfield to make him their record signing this summer. The Belgian winger was simply scintillating against Huddersfield when he came off the bench in the Blues' 3-0 win, away from home.
"From the physical point of view, it's different", the Chelsea boss said, comparing the Premier League to Serie A.
Willian's cross to the back post was testing, and there was Kante to half-volley in for just his third Premier League goal for Chelsea - scoring one in each of his three seasons. The team has to head to Manchester City next week.
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