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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13. SUB: Lyle Foster - 6/10
For Anthony, 71 Could be an option on the left wing moving forward given the mixed recent form of Jaidon Anthony. (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk
14. SUB: Armando Broja - 6/10
For Flemming, 71 Looks sharper, but chances were minimal during his time on the pitch. Relief his injury wasn't a serious one. (Photo by Nathan Stirk/Getty Images) Photo: Nathan Stirk
15. SUB: Jacob Bruun Larsen - 6/10
For Tchaouna, 76 Tried to get things going down the right flank during the final stages, but it was too little, too late. (Photo by Dan Istitene/Getty Images) Photo: Dan Istitene
16. SUB: Josh Laurent - 6/10
For Florentino, 84 Only had minimal time on the pitch to make an impact, but Burnley were certainly in need of fresh legs. (Photo by ANDY BUCHANAN / AFP via Getty Images) Photo: ANDY BUCHANAN