Tuchel replaced Frank Lampard as head coach earlier this week and began his reign with a 0-0 draw with Wolves on Wednesday.
So which players stood out most in Chelsea's win over Sean Dyche's team?
✔️ GOOD PERFORMANCE
Cesar Azpilicueta: 8.4
The Chelsea captain led by example by scoring the first goal of Tuchel's reign with a ferocious finish.
A free-flowing Chelsea move involving Jorginho, Mason Mount and Callum Hudson-Odoi ended with Azpilicueta thumping the ball past Nick Pope.
The Spaniard seems to be enjoying playing in a back-three again, having excelled in the system under previous manager Antonio Conte. That's now two straight clean sheets for Chelsea under Tuchel.
❌ BAD PERFORMANCE
Tammy Abraham: 5.4
The young English striker was handed his chance from the start against Burnley, having been a substitute to Olivier Giroud against Wolves.
However, he failed to grasp his opportunity and was taken off at half-time by Tuchel after a disappointing first-half performance.
He had no shots, no dribbles, no chances created and only five attempted passes as he simply failed to get into the game.
⭐ STAR MAN
Thiago Silva: 8.5
The veteran Brazilian has been one of the few successes from Chelsea's €250 million splurge last summer - and he didn't cost a dime in transfer fees!
Thiago Silva put in a flawless performance at Stamford Bridge as Burnley didn't register an attempt of any kind until injury time.
He made a match-high 15 recoveries and four interceptions as he demonstrated that he is still one of the best readers of the game.