Trailing to a goal from Wilson Odobert in the first half, the Londoners responded with four goals to record back-to-back league wins for the first time since March and a third straight victory in all competitions.
An own-goal from Ameen Al Dakhil evened the score at halftime and Chelsea took the lead through Cole Palmer’s penalty after the break. Raheem Sterling and Nicolas Jackson also struck to complete the rout.
On the back of Monday’s 2-0 win against Fulham, Chelsea were looking to build on only their second victory in the league this season.
But they were trailing to Odobert’s goal in the 15th when he shot between Marc Cucurella and goalkeeper Robert Sanchez.
Chelsea equalized when Sterling’s cross took a deflection off Al Dakhil to loop into the net in the 42nd.
Sterling was fouled by Vitinho on the edge of the box at the start of the second half and referee Stuart Attwell pointed to the spot. After a lengthy check from VAR, Palmer converted the penalty for his first Chelsea goal.
Chelsea extended their lead in the 65th when Conor Gallagher picked out the run of Sterling and he finished confidently.
Burnley fans started to head for the exits in the 74th when Sterling crossed to Palmer, who found substitute Jackson. He skipped away from Dara O’Shea in front of goal before scoring.