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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9. Loum Tchaouna - 6/10
Started off brightly, seeing an early shot blocked and testing the keeper with a curling, long-range effort. But ran out of energy and faded. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
10. Jaidon Anthony - 6/10
Got into some good positions early on but just took a little too long, which allowed Chelsea men to make the blocks. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
11. Zian Flemming - 6/10
Didn’t see a great deal of the ball, with his one and only chance coming immediately before he was withdrawn, lashing over after cheating the ball down. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
12. SUB: Hannibal - 6/10
For Ugochukwu, 71 Added some freshness and impetus as Burnley chased a late equaliser. (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk