Sarri, who became the club’s 10th full-time manager in 10 years when he replaced the sacked Antonio Conte in the summer, saw his side take the lead with their first shot on target.
It came in the 34th minute when N’Golo Kante’s mis-hit strike from Willian’s cross bounced past Huddersfield goalkeeper Ben Hamer.
Jorginho followed Sarri from Napoli to Chelsea in the summer and the midfielder doubled the Blues’ lead when he converted a penalty after Christopher Schindler fouled Marcos Alonso.
Pedro sealed a comfortable win with a cool, chipped finish for Chelsea’s third after being played in by substitute Eden Hazard.
Before the second goal, the Terriers had hit a post through Steve Mounie’s header, but it was to be Sarri’s and Chelsea’s day.