Chelsea had their first real chance at goal 11 minutes in when Cesar Azpilicueta's low cross was deflected and almost sat up for Willian to fire home in the centre of the goal.
Gary Cahill meets Soccer AM's Tubes to discuss all things Chelsea.
Then it was a case of terrible defending that saw the visitors race into a 3-0 lead.
Alvaro Morata made his debut, and was chopped down for a yellow card by Ben Mee in the 64th minute.
The main attacking outlet for the Blues was on the right with Cesar Azpilicueta sending in deadly balls.
Jermain Defoe came on for Bournemouth after the break, replacing Benik Afobe, but the former Sunderland striker had little to work with as West Brom held firm.
Then on 14 minutes skipper Gary Cahill took the ball forward, but lost control of the ball and challenged Steven Defour.
Conte believes that he might need to train his players with one or two men fewer after the spate of red cards they have received in recent games but he didn't want to talk about the referee's performance.
Vokes put Burnley ahead in the 24th minute, volleying in from Matthew Lowton's cross.
Chelsea did their best to launch a positive response, but the Blues were struggling, and Burnley incredibly doubled their lead in the 39th minute when Stephen Ward broke into the home side's box before finding the top corner with a stunning strike.
Incredibly three minutes later and it's 0-3.
There were no change at half time by either side.
It was a dispiriting afternoon for Conte, who won the title in his first season at the club but has complained that Chelsea have not signed enough new players while allowing several to leave.
The Blues forced goalkeeper Tom Heaton into a couple of smart saves, in a hope of regaining a foothold in the match.
Turns out Morata can play, and his diving header met a classy bit of playmaking from Willian to make it 3-1 in the 69th minute.
Chelsea thought they had a second on 72 minutes.
Soon after, Vokes had a goal called offside. "I don't know if Pedro will have recovered for the next game but for sure we will have two players banned, Cahill and Fabregas".