Eden Hazard sent the home side into a ninth-minute lead with a curling effort from distance, before Willian and Victor Moses added a second and third during what was a comfortable afternoon for Antonio Conte's side.
Willian was fit to return to the Chelsea XI and took the place of Pedro as Conte made one change to the team that beat Watford last weekend, while Burnley were unchanged from their 2-0 victory over Liverpool last time out.
Chelsea were the more forward-thinking outfit in the early exchanges and had the lead in the ninth minute of play when Hazard drove to the edge of the Burnley box before curling his effort into the bottom corner past Tom Heaton.
Hazard had a golden chance to score a second just six minutes later when the Belgian once again found space inside the Burnley box, but Ben Mee was on hand to clear off the line, before Gary Cahill just missed the target with a volley.
The visitors just could not get into the match as Chelsea dominated, and Burnley stopper Heaton had to keep out a John Terry header just before the 30-minute mark as the one-way traffic continued at Stamford Bridge.
Seven minutes before the break, the home side had another golden chance when Hazard collected a pass from Willian before setting up Diego Costa inside a crowded Burnley box, but the Spaniard could only fire straight at Heaton.
Chelsea had their second in the 42nd minute, however, when Costa found Willian in a wide position and the Brazilian took a touch outside his full-back before drilling the ball across Heaton into the corner of the net.
Burnley's only real chance of the first half came two minutes before the break when Scott Arfield found space down the right before drilling the ball towards the far corner, but his effort just missed the post.
Willian stood over a 25-yard free kick in the 51st minute as Chelsea had the opportunity to score a third, but the Brazilian just missed the crossbar, before Heaton did well to keep out another close-range effort from Costa.
Chelsea had two more opportunities just before the hour as Heaton was forced down low to keep out a volley from Hazard and the rebound fell to Terry, who somehow fired over the crossbar from close range.
Heaton continued to impress between the sticks for Burnley as the goalkeeper, who travelled with the England squad for Euro 2016, kept out Hazard with little under 30 minutes of football to play in the capital.
Burnley had more ambition in the final 15 minutes as they looked to set up a grandstand finish, but Chelsea were always comfortable as they eased their way to another three points, which took them to the top of the division.
There was time for one more goal, meanwhile, as the three substitutes - Michy Batshuayi, Pedro and Moses - all combined, and it was Moses that converted at the far post to make it 3-0.
Next up for Chelsea is a trip to Swansea City after the international break on September 11, while Burnley will attempt to return to winning ways when they welcome Hull City to Turf Moor on September 10.