Another simple short free-kick saw the ball pinged into the Chelsea penalty area and unmarked Vokes smashed home a powerful header into the ball of the net.
But that soon changed as new boy Alvaro Morata, a £60million buy from Real Madrid, entered the fray on 58 minutes, replacing ineffectual Michy Batshuayi.
That wouldn't be the end of the harsh vibes at the Bridge, and Stephen Ward scored a goal Burnley fans will never forget when he laced a gorgeous shot from an unlikely and tight angle to make it 2-0.
The victory was Burnley's first on the opening day of the top flight in 44 years, and it comes after they had to wait until their 18th away game to record a first success on the road last season.
But Burnley could have got a fourth but Robbie Brady's free kick rebounded off the post.
It has not been a good start to the season for the Blues, with Conte's men having also lost to Arsenal in the Community Shield at Wembley last weekend.
Conte made a tactical reshuffle after Cahill's exit, Andreas Christensen coming on for Jeremie Boga, who had been named a surprise debutant due to Pedro's injury.
The Blues trailed Burnley by three goals in the opening 45 minutes - and although they mustered a comeback in the second half, they only succeeded in making the scoreline look respectable at 2-3. Five minute later Vokes met Steven Defour's cross to power home the third. A quick free-kick led to Defour swinging in a cross from the right and an unmarked Vokes planted a header past Courtois, with loud boos greeting the champions when the half-time whistle was blown.
At 3-0 down and going into the second-half there was little inspiration for manager Antonio Conte to turn to on the bench.
Chelsea went down to nine men via a red card to Fabregas with about 10 minutes to go.
But David Luiz then gave the Blues further hope, rifling a volley past Heaton after racing on to a Morata flick-on. However, David Luiz ensured a tense finish when he volleyed home in the 88th after being teed up by the influential Morata.