Fresh from the news that Roman Abramovich will sell the club, Chelsea needed a second half onslaught after a goalless first half to break Burnley's resistance.
Three goals in the opening nine second half minutes from Reece James and a Kai Havertz brace put daylight between the two sides before Cristian Pulisic added gloss on the scoreline with a fourth.
Aston Villa put away in-form Southampton 4-0 at Villa Park thanks to goals from Ollie Watkins, Douglas Luiz, Danny Ings and Philippe Coutinho.
Newcastle United put some daylight between themselves and the relegation zone with a vital 2-1 win over Brighton and Hove Albion while an Ivan Toney hattrick helped Brentford beat Norwich City 3-1 at Carrow Road.
Crystal Palace recorded a 2-0 win at Wolverhampton Wanderers after first half goals from Jean-Philippe Mateta and Wilfried Zaha.
In the early kick-off, Jesse Marsch's first game in charge of Leeds United ended in defeat as Leicester City won 1-0 at the King Power Stadium.
