Chelsea, who had club captain Gary Cahill and Cesc Fabregas sent off, trailed 3-0 at the interval, and despite finding a route back into the match in the second period, Burnley held on for their first ever Premier League victory at Chelsea.
New skipper Gary Cahill was shown a straight red card in only the 14th minute for a high boot on a reckless challenge.
"I have had only two pre-season games, 15 competitive minutes and a missed penalty. and they're already killing me, so I know what's ahead".
Burnley did not take long to make their numerical advantage count as full-back Matt Lowton's cross from the right was hooked goalwards by Vokes, the ball taking a slight touch off David Luiz before beating the scrambling Thibaut Courtois.
The visitors were the better side overall with a disciplined, energetic and ruthless first-half display that saw them put three past the Blues, with Sam Vokes netting twice.
Chelsea improved after halftime.
It was a nervous time for Burnley fans as Chelsea continued to press.
An increasingly frustrated and vitriolic home support attempted to instigate the beginnings of a Chelsea turnaround, raising the noise levels as Chelsea searched for a goal back.
The Spanish forward thought he had another minutes later, but his close range finish was ruled out for offside.
The Blues came out with renewed vigor in the second half, pressing their opponents as they looked to reduce the three-goal deficit, but the champions were still lacking in the final third. But Chelsea weren't finished.
Leicester City lost 2-1 at Hull City on the first day last season, but given the unexpected nature of their title win, this was the biggest opening-day shock since Manchester United's 3-1 loss at Aston Villa in 1995.
Chelsea striker Alvaro Morata broke the club transfer fee record when he signed last month, creating massive expectations at Stamford Bridge.