Having gone down to 10 men following Gary Cahill's red card after 15 minutes, Sam Vokes gave the away side a surprise lead, before Irish defender Stephen Ward doubled his side's advantage with a stunning half-volley from the edge of the box. Alvaro Morata, on as a second-half substitute, reduced the deficit in his first league start since a club-record move from Real Madrid for £58 million (NZ$103 million).
Any hopes of an unlikely comeback looked to have disappeared when midfielder Cesc Fabregas was red-carded in the 81st after receiving his second booking.
Asked whether he sensed the champions were vulnerable without Eden Hazard, Diego Costa, Pedro and Tiemoue Bakayoko, he added: "I don't think so".More news: US Muslim Wins Payout After Hijab 'Forcibly Removed' by Police
And Conte says he isn't anxious about his squad depth. Little contact was made, but intent was enough for a sending off.
"First half better, second half not as well, but they're a good side - their physicality, they're a strong side, they press high, fast, and it can put you off kilter".
Kick-off is just under a half hour from now.More news: Trump Pressures China On Trade; Executive Action Expected Monday
Burnley went for the fourth goal but the post kept out a 90th minute freekick as the defending champions sought an equaliser.
Nevertheless, Burnley managed to see out the closing stages to claim a famous victory at Stamford Bridge. Vokes had a goal disallowed shortly after - but it was an omen for Chelsea.
"A lot was made of our away form last season", Vokes said.
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