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.