The Blues dominated the first half, and Disasi had a goal ruled out by VAR for handball before Palmer gave them the lead. Mudryk was brought down in the box by Assignon, and the referee pointed to the spot before sending the Frenchman off for his second booking, which was quickly followed by a red card for Kompany for dissent.
Palmer scored a wonderful Panenka from the spot to put them in front, but Burnley pulled level just two minutes after the break through Cullen’s long-range strike.
Muric made vital saves to keep his side in it before Palmer eventually got his second of the game with a drilled finish, but just three minutes later, O’Shea thumped in an equaliser.
Sterling missed a sitter, while Rodriguez struck the bar as both teams searched for a winner, but there was nothing to separate the sides.
Chelsea went off to boos from the home fans and now turn their attention to Manchester United on Thursday as they stay in 11th. Burnley are still 19th but are now four points from safety. They host Wolves on Tuesday.
