Premier League leaders Chelsea were made to regret missed chances as Matej Vydra rescued a point for Burnley.
Kai Havertz opened the scoring for Chelsea with a header from Reece James' cross, only his second league goal this season.
That is the seventh Premier League goal that right-back James has been involved in in six starts this season.
The Blues could have scored a hatful with Thiago Silva's header hitting the post, while Nick Pope saved well from Callum Hudson-Odoi in each half.
But Burnley levelled when Ashley Westwood whipped in a cross which Jay Rodriguez headed across to Vydra to stab home.
Chelsea are three points clear of Manchester City at the top of the table, while Burnley remain in the relegation zone.
Chelsea's run of four Premier League wins in a row - and seven consecutive victories in all competitions including penalty shootouts - comes to an end and manager Thomas Tuchel will be wondering how.
His side have coped well without the injured striker Romelu Lukaku in recent weeks, but they could have done with him here.
It was not looking that way when James whipped in a cross for Havertz to score.
They ended with 25 shots, but only four on target.
The European champions had a host of chances in both halves - with headers from Andreas Christensen, Antonio Rudiger, Jorginho, Havertz and Silva all going close.
Ross Barkley, on his first league start for the club since 2019-20, was wayward with several shots.
Burnley created very little until the 70th minute when they started to improve and, while Vydra's goal was not inevitable, it was not completely against the run of play.
The visitors could have won it too. Jay Rodriguez lacked conviction in injury-time when he headed for the corner flag instead of going for goal, and Vydra hit a half-volley wide from a long Pope clearance.
Coming on the back of their first win of the Premier League season - against Brentford last weekend - Clarets boss Sean Dyche will be optimistic his side can, once again, push up the table after a slow start.
helpHow to play
Rate players out of 10 throughout or after the game. The rater will close 30 minutes after the final whistle.
Rating range key1 = Give it up10 = Pure perfection
Chelsea
Squad number16Player nameMendy
Squad number4Player nameChristensen
Squad number6Player nameThiago Silva
Squad number2Player nameRüdiger
Squad number24Player nameJames
Squad number7Player nameKanté
Squad number5Player nameJorginho
Squad number21Player nameChilwell
Squad number18Player nameBarkley
Squad number20Player nameHudson-Odoi
Squad number29Player nameHavertz
Squad number10Player namePulisic
Squad number12Player nameLoftus-Cheek
Squad number19Player nameMount
Burnley
Squad number1Player namePope
Squad number2Player nameLowton
Squad number5Player nameTarkowski
Squad number6Player nameMee
Squad number3Player nameTaylor
Squad number7Player nameGudmundsson
Squad number18Player nameWestwood
Squad number8Player nameBrownhill
Squad number11Player nameMcNeil
Squad number20Player nameCornet
Squad number9Player nameWood
Squad number19Player nameRodriguez
Squad number23Player namePieters
Squad number27Player nameVydra
Line-ups
Chelsea
Formation 3-4-1-2
16Mendy
4Christensen6Thiago Silva2Rüdiger
24James7Kanté5Jorginho21Chilwell
18Barkley
20Hudson-Odoi29Havertz
16Mendy4Christensen6Thiago Silva2Rüdiger24JamesBooked at 76mins7KantéSubstituted forMountat 85'minutes5Jorginho21Chilwell18BarkleySubstituted forLoftus-Cheekat 73'minutes20Hudson-OdoiSubstituted forPulisicat 85'minutes29HavertzSubstitutes
1Arrizabalaga10Pulisic12Loftus-Cheek14Chalobah17Saúl19Mount22Ziyech28Azpilicueta31SarrBurnley
Formation 4-4-2
1Pope
2Lowton5Tarkowski6Mee3Taylor
7Gudmundsson18Westwood8Brownhill11McNeil
20Cornet9Wood
1Pope2Lowton5TarkowskiBooked at 84mins6Mee3Taylor7GudmundssonSubstituted forVydraat 70'minutes18WestwoodBooked at 68mins8BrownhillBooked at 90mins11McNeil20CornetBooked at 76minsSubstituted forPietersat 88'minutes9WoodSubstituted forRodriguezat 61'minutesSubstitutes
4Cork10Barnes13Hennessey14Roberts19Rodriguez22Collins23Pieters27Vydra28LongLive Text
Match ends, Chelsea 1, Burnley 1.
Second Half ends, Chelsea 1, Burnley 1.
Attempt missed. Matej Vydra (Burnley) right footed shot from outside the box misses to the left. Assisted by Nick Pope.
Corner, Chelsea. Conceded by Erik Pieters.
Foul by Dwight McNeil (Burnley).
Ben Chilwell (Chelsea) wins a free kick on the left wing.
Josh Brownhill (Burnley) is shown the yellow card for a bad foul.
Christian Pulisic (Chelsea) wins a free kick in the defensive half.
Foul by Josh Brownhill (Burnley).
Offside, Burnley. Charlie Taylor tries a through ball, but Matej Vydra is caught offside.
Foul by Reece James (Chelsea).
Jay Rodriguez (Burnley) wins a free kick on the left wing.
Substitution, Burnley. Erik Pieters replaces Maxwel Cornet.
Attempt missed. Thiago Silva (Chelsea) left footed shot from the centre of the box is high and wide to the left. Assisted by Andreas Christensen following a corner.
Attempt blocked. Antonio Rüdiger (Chelsea) left footed shot from the centre of the box is blocked. Assisted by Ben Chilwell.
Corner, Chelsea. Conceded by Ashley Westwood.
Offside, Burnley. Nick Pope tries a through ball, but Matej Vydra is caught offside.
Attempt blocked. Ben Chilwell (Chelsea) left footed shot from the centre of the box is blocked.
Attempt blocked. Thiago Silva (Chelsea) header from a difficult angle on the right is blocked. Assisted by Mason Mount with a cross.
Corner, Chelsea. Conceded by Jay Rodriguez.
Our coverage of your Premier League club is bigger and better than ever before - here's everything you need to know to make sure you never miss a moment