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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1. Martin Dubravka - 6/10
Not much he could do about either goal. Appeared to get the slightest of touches to turn Neto’s shot onto the post. Dealt with aerial bombardment pretty well. (Photo by ANDY BUCHANAN / AFP via Getty Images) Photo: ANDY BUCHANAN
2. Kyle Walker - 6/10
Stopped a certain Chelsea goal with his back post clearance, but given one or two problems by the tricky Jamie Gittens. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
3. Axel Tuanzebe - 6/10
Pretty solid in the main, but will be disappointed with the manner of Chelsea’s late second, where he was turned a little too easily by Marc Guiu. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
4. Maxime Esteve - 8/10
Burnley’s standout man by far. Immense in the first-half in particular, making a number of key interceptions. Always in the right place at the right time. (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk