Hakim Ziyech fired the Blues into the lead in the 27th minute when firing low past Nick Pope from inside the penalty area.
Kurt Zouma towered above James Tarkowski to convert Mason Mount's corner just after the hour.
And then Timo Werner ended the game as a contest when sliding the ball past Pope after being picked out by Ziyech.
1. Nick Pope 5
The goalkeeper had seemingly shifted his weight on to his right foot when failing to keep out Ziyech's effort. Left exposed for Chelsea's second and it was a similar story for the away side's third.
2. Matthew Lowton 5
Often chasing shadows as Chelsea stretched the play and manipulated space with ease. Caught out by Chilwell's advances forward as the Blues dropped passes in behind and Werner would capitalise when the full back was pulled out of position.
3. Charlie Taylor 5
Had his work cut out when attempting to stay narrow and compact as the visitors came forward, leaving James with acres of space in behind. Ziyech also caused the full back endless problems when picking up pockets just in front.
4. Kevin Long 5
Stayed compact centrally as Chelsea saw plenty of the ball in and around the Burnley box. Made a couple of timely challenges to prevent the likes of Werner getting clear, but dominated by Abraham in the air.