Chelsea defender Antonio Rudiger and Burnley goalkeeping coach Billy Mercer had to be separated by the officials at the final whistle, as a gripping encounter ended in ugly touchline scenes at Stamford Bridge.
Defender Luiz and Ashley Westwood later clashed as the teams attempted to depart via the tunnel, in a frantic west London encounter.
Luiz told Sky Sports: "We tried everything to win the game.
"It's difficult when you play against a team who have two chances and score two goals and didn't want to play the game.
"It's anti-football. Losing time [time wasting] all the time, especially when you have the ball. Their players went to the floor and stopped the game.
"They were playing 11 inside the box. It's difficult to score against a team like that."