Wilson Odobert put Burnley ahead early on but Chelsea dragged themselves level with an own goal from Ameen Al Dakhil shortly before half-time, and the Blues ran away with proceedings after the break.
The inspired Raheem Sterling won a penalty which was finished off by Cole Palmer, before the winger added a goal of his own, and Nicolas Jackson popped up with a fourth to cap off a memorable victory for Mauricio Pochettino’s side.
The first sight of goal came eight minutes in as Palmer spun his defender on the edge of the box, but the summer signing’s effort from range flew high and wide.
Burnley were lively on the counter but lacked composure in the final third, passing directly out of play or running out of steam and conceding possession far too easily, although the signs of Burnley’s threat were clear early on.
After watching Sterling curl wide, Burnley put the pieces together and fired themselves ahead as Odobert’s low effort trickled into Robert Sanchez’s bottom corner.
It could have easily been 2-0 soon after Odobert’s cross caught Levi Colwill sleeping at the back post, but the onrushing Mike Tresor couldn’t steer an effort on target.
Chelsea’s response was slow and predictable. The Blues spent most of the first half passing around the back, with Burnley happy to deal with the long balls and crosses that inevitably followed.
Shortly before half-time, Sterling helped produce an equaliser. His fizzed cross struck the hip of Al Dakhil, whose deflection soared over James Trafford and into the back of the Burnley net.
Chelsea brought a little more energy in the second half and were awarded a penalty just three minutes in when Sterling was scythed down by Vitinho, and up stepped Palmer to slot home from 12 yards.
Enzo Fernandez sent a tame effort straight at Trafford, but Sterling was far more convincing in front of goal as he fizzed a strike beyond Trafford to hand Chelsea an imposing lead shortly after the hour mark.
It was four ten minutes later as substitute Jackson slotted home from inside the box, marking the first time Chelsea have scored four goals in a single game since April 2022.