Cole Palmer and Noni Madueke's quality shone through the fight produced by a spirited Luton Town fightback.
The duo ran riot in the first half at Kenilworth Road, with Palmer thumping in an excellent finish to open the scoring after Issa Kabore's calamitous pass out from the back.
Madueke added a second just before half-time, smashing a finish beyond Kaminski. Palmer rounded the Luton goalkeeper in the second half but Ross Barkley and Elijah Adebayo headers threatened an historic Chelsea collapse.
But Chelsea ultimately outgunned Luton to seal an important victory to close out a difficult 2023.
Noni Madueke's unwavering confidence lifts Chelsea
Palmer's excellence could be matched by Noni Madueke, who has shown great personality and belief to force himself back into the team.
The 21-year-old winger had every reason to feel insecure or lacking in confidence, having only started once in the league, but it hasn't impacted him one bit.
Since his return from a minor muscle injury, he has been flying. A sensational match-winning 20-minute cameo at home to Crystal Palace was followed up by a positive display starting ahead of Raheem Sterling at Kenilworth Road.
He created a big chance for Conor Gallagher early on before he dribbled past Alfie Doughty to smash in Chelsea's second.
His confidence in himself was shown by his baiting salute celebration in front of the home crowd.
He has an unwavering belief that he should start for Chelsea and if he keeps playing like this, then he will be impossible to ignore.
Petrovic is Chelsea's new no1
The two-time Serbia international was a relative unknown in European football before arriving at Chelsea, but he has slotted in seamlessly.
Robert Sachez's knee injury could have been a calamity, but the Blues have now shown they have a high-quality no2.
He could soon be considered a no1, with Luton testing his ability to come for crosses in open play and at set-pieces.
Petrovic's best save yet was a one-handed stop from Carlton Morris during a late aerial bombardment that threatened a Chelsea collapse.
He conceded twice but that owed more to the volume of crosses, with goals an inevitability.
Self-destruct mode almost pressed
Rob Edwards's side fully deserved their late Ross Barkley and Elijah Adebayo goals, which formed just part of an aerial attack on Chelsea's defence.
The midfield and full-backs offered little protection from wide areas, with 36 crosses launched into the box.
It was an uncontrolled end to what should have been a positive afternoon, with substitutions like the late addition of a half-fit Christopher Nkunku almost causing Chelsea to throw it away.
The three points should still be celebrated, but that self-destructive streak remains.
