Christian Pulisic scored his first goal for the Blues but a mistake from Matthew Lowton saw the American steal the ball, before he burst forward, kept his calm and coolly slotted home to put the visitors in front inside 20 minutes.
The Blues doubled their lead just before half time, as Pulisic scored his second of the game.
It was another piercing run through the Burnley defence, as he got through and fired his shot into the bottom corner to give Chelsea a comfortable lead going into the break.
Frank Lampard’s side started the second half as they ended the first, and made it three soon after the restart.
Mason Mount put the ball back into the box with a delightful ball, and Pulisic was there to head it into the roof of the net to secure his first-ever hat-trick.
Just two minutes later, Willian put the game to bed with a wonderful low finish after Tammy Abraham put him through on goal.
Chelsea thought they had a penalty, but VAR overturned Michael Oliver’s decision as substitute Callum Hudson-Odoi was booked for simulation.
Burnley scored two cracking consolations with minutes left on the clock, thanks to excellent strikes from Jay Rodriguez and Dwight McNeil.
However, it wasn’t enough for the hosts, as Chelsea secured an emphatic win at Turf Moor.