Chelsea took the lead at the break through Jorginho’s penalty as he put the penalty away in trademark style, waiting to see where the goalkeeper was going before placing it in the opposite corner.
Tammy Abraham’s header doubled the lead for the home side after James cross from the right met the forward unmarked in the box.
Burnley had a Hendrick goal ruled out for offside as well as Mee’s effort blocked off the line by Barkley.
Callum Hudson-Odoi then stepped in to make the score 3-0 for Frank Lampard’s men.
Azpilicueta whips a cross in towards the back post and Hudson-Odoi arrived to steer in Chelsea’s third to make sure its game over for Burnley.
The win see the Blues maintain their 4th spot on the Premier League with 39 points.