A late equaliser from substitute Matej Vydra saw the Clarets take a point off European champions Chelsea at Stamford Bridge.
The Premier League leaders had broken the away side's resolve in the 33rd minute when Kai Havertz got on the end of a Reece James cross.
The Blues had ample opportunities to score either side of the German forward's finish, but were unable to find a way past Nick Pope.
And they became the victims of Burnley's smash and grab in the 79th minute as Vydra converted from close range.
The Czech Republic international coolly lifted the ball over Edouard Mendy after fellow substitute Jay Rodriguez had guided Ashley Westwood's whipped cross into his path.
It was the sixth point that Sean Dyche's side had collected from their last seven top flight trips to SW6.
1. Nick Pope 8.5
Were you watching Gareth Southgate? The goalkeeper reacted well to keep out Hudson-Odoi and Havertz early on and then made the save of the match with his legs when Taylor had diverted James's cross goalwards. Made a second save with his legs to deny Hudson-Odoi after the break. Photo: Ryan Pierse
2. Matt Lowton 7.5
Havertz managed to get in behind a couple of times, and the full back was forced to stretch his legs as Chilwell broke forward at every opportunity, but nothing of note was generated down that side of the pitch for the Blues. Did just about enough to prevent Havertz from hitting the target in the second half. Photo: Ryan Pierse
3. Charlie Taylor 8
Failed to press the ball when James provided the assist for Chelsea's opener, but was largely impressive otherwise. Made a number of timely blocks and interventions in both halves to help keep the Clarets in the game. A tireless display up against the home side's in-form right back. Photo: Alex Pantling
4. James Tarkowski 7
Uncharacteristically slack at times in his defending, especially from set-pieces. Rudiger managed to wriggle free and head over from corners twice, he was unable to get close to Havertz for the goal and was caught out by Silva as the Brazilian clipped the outside of the post. Photo: Ryan Pierse