The Blues received a boost for the top four after Arsenal, Tottenham and Arsenal lost at the weekend.
But Chelsea fell behind in the first half as early as the 8th minutes before Kante equalized. The club then went ahead with a well-taken Higuain goal before conceding few minutes later.
Hopes of a goal-fest evaporated in the second half with Burnley shutting down all the attack threats of Chelsea to leave the Sarri-coached team rooted on fifth with the same point as Arsenal.