The Blues opened the scoring through Pedro but the Republic of Ireland winger levelled the affair with a beautiful free-kick
Chelsea missed the chance to move 12 points clear at the top of the Premier League as Robbie Brady's stunning free-kick earned a 1-1 draw for Burnley at Turf Moor.
With Tottenham losing 2-0 at Liverpool on Saturday, the door was left open for runaway leaders Chelsea to extend their advantage.
And Antonio Conte's men were fast out of the blocks, with Pedro applying the finish to a lightning counter-attack in just the seventh minute.
However, 28 of Burnley's 29 points prior to the match had come at home this season and Sean Dyche's men put in a typically full-blooded display that yielded an equaliser through Brady's exquisite free-kick on his first start for the club.
Chelsea peppered the Burnley box, but the Blues failed to break down a stubborn home defence and Burnley arguably had the better chances to win the game, with Matt Lowton and Andre Gray missing fine opportunities.
Despite the draw, Chelsea are now 10 points clear of Arsenal and Spurs, while Burnley are rewarded for their endeavour by moving up a place to 12th.
Chelsea threatened early when Eden Hazard raced onto Diego Costa's sublime throughball before shooting tamely at Tom Heaton.
Burnley failed to heed the warning, though. Hazard launched a counter to Victor Moses on the right and he finished a mazy run with a deflected pass that found Pedro, who took a touch and coolly slotted into the bottom left-hand corner.
The match was being played at a quick tempo, but Chelsea had been largely untroubled until Nemanja Matic fouled Joey Barton 25 yards from goal.
Brady lined up the resulting free-kick and curled a stunning effort into the top-left corner of the Chelsea goal.
The Blues continued to enjoy a near monopoly on possession without troubling Burnley's goal and Courtois had to make a smart stop with his legs at the other end after Barton slipped in Lowton.
Some uncharacteristically slack Chelsea defending led to a gilt-edge Burnley chance early in the second half.
Gary Cahill - making his 150th league appearance for Chelsea - was beaten to Matic's poor header by Ashley Barnes before David Luiz failed to cut out his weak pass, but Gray shot tamely at Courtois when one-on-one.
Ben Mee was fortunate that his dawdling on the ball did not lead to a clear shot for Costa, but in general Burnley were superb in defence against relentless pressure and, aside from a long-range Cesar Azpilicueta effort that just cleared the crossbar, Chelsea had little to show for their labours.
As the clock wound down, Conte threw on Willian and Cesc Fabregas and switched from his favoured 3-4-3 to a 4-4-2 formation.
The Blues continued to attack in numbers and Pedro perhaps should have done better with a bending shot from the left of the area.
No winner was forthcoming, though, as Burnley claimed a hard-fought point with just their third draw of the season.