The Clarets were more than a match for the second-placed Blues, who now move within three points of league leaders Arsenal
In fact, Scott Parker’s men were the better side during the first-half, but cruelly found themselves going in behind due to Pedro Neto’s back post header.
The hosts had otherwise looked the more threatening, finding themselves in dangerous positions on a number of occasions, only to lack that decisive bit of quality in the key moments.
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The Clarets also felt they ought to have been awarded a penalty prior to Neto’s opener in a bizarre incident, where Trevoh Chalobah handled the ball after goalkeeper Robert Sanchez had taken a short goal kick to him.
Burnley huffed and puffed during the second-half, but just as they appeared to be launching a late onslaught – Enzo Fernandez added a late second to put the game to bed.
Here’s how Burnley’s players rated:
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5. Quildindshy Hartman - 6/10
Drawn into the centre for Chelsea's opening goal, allowing Pedro Neto to coast in behind him. But otherwise defended resolutely, without having too many opportunities to get forward. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
6. Florentino Luis - 6/10
Got through plenty of defensive work, as is now customary. Wayward with one or two passes though. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
7. Josh Cullen - 6/10
Helped pull the strings as Burnley did all the early running, but influence faded as the game wore on. Picked up a harsh booking. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
8. Lesley Ugochukwu - 6/10
Started off well with some smart link-up play, but otherwise struggled to get himself in the game against his former club. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard