Burnley's lead was doubled when, with a little over five minutes remaining until the break, Jack Cork set up Stephen Ward to hammer home, and it was 3-0 before the interval when Vokes scored his second with a header.
With the Blues struggling up front, Conte introduced Alvaro Morata for his league debut, with the in-effective Michy Batshuayi making way.
A sense of injustice spurred on Chelsea's riposte, which only grew when Cesc Fabregas became the second player to walk, for a second yellow card, less than ten minutes after substitute Alvaro Morata had reduced the arrears to 3-1.
Chelsea's Gary Cahill checks that Steven Defour of Burnley.
The Chelsea manager told the BBC: "The sending off of Cahill was a key moment, because to play the rest of the game with 10 and then nine men is not easy".
Vokes' second goal came just before the half as he found himself unmarked in the centre of the goal and flashed a header beyond the despairing Courtois. "It was a pity because our fight in the second half was very good", he said.
"We have to improve a lot on this because after the first red for Cahill we lost our composure and conceded three".
Morata, he said, was working hard on his fitness and on adapting to Conte's system.
With the Blues and Liverpool returning to European football, and all top six clubs strengthening considerably in the transfer market along with Everton, Cahill believes the title race will be more open than ever. I am ready to fight with these players.
"I'm not anxious because we have to trust in our work".
In the end, there was no third goal for the nine men. Fabregas departs. Not the greatest of starts for the champions.
"Our mentality I was really pleased with, to see the game through".
Huddersfield Town marked their top flight return with a remarkable 3-0 win at Crystal Palace that sent them top of the table, while Wayne Rooney bagged the victor on his Everton comeback in a 1-0 victory over Stoke City. "And it was weird at half-time because you're three up away at Chelsea and you have to decide how you're going to approach it from there", he added.
"Winning away from home on the first days quietens down some stories - we're written off at the start of every season".
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