Captain Gary Cahill was sent off after just 14 minutes for a challenge on Steven Defour, but that was just the start of the astonishing drama at Stamford Bridge.
Sam Vokes starred for Burnley with two of his side's three goals before half-time, Stephen Ward also netting in between the Wales striker's double.
In-form Vokes now has seven goals in his last six Premier League appearances after netting only five in the previous 58.
Antonio Conte gave Alvaro Morata 31 minutes from the substitutes' bench on his Premier League debut and he scored with a header.
Any hopes of a recovery were dented when Cesc Fabregas was sent off after collecting a second booking late on, although David Luiz did set up a grandstand finish with a powerful volley to make it 3-2 with two minutes left. Robbie Brady then hit the post at the opposite end from a free-kick as Burnley pushed for a fourth.
The unexpected result is Chelsea's first opening-day defeat for 19 years and only the second time the Premier League's defending champions have lost their first game in 26 years.
Cahill's early departure stunned Stamford Bridge, the defender taking a heavy touch and diving forward with his boot raised in a bid to win back possession against Defour, with referee Craig Pawson immediately brandishing a straight red.
It was the third consecutive competitive match in which the Blues have received a red card, having had Victor Moses sent off in May's FA Cup final and Pedro removed in last week's Community Shield, both games against Arsenal.
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.
Vokes had a header ruled out after James Tarkowski was penalised for a foul in the build-up, but Burnley soon scored a goal that did count as Chelsea's afternoon took another turn for the worst after 24 minutes.
Matt Lowton's right-wing cross found Vokes and he sent a bouncing volley into the far corner, with Thibaut Courtois unable to get across in time.
Burnley doubled their lead after 39 minutes, Ward playing a one-two with Jack Cork before unleashing an excellent half volley into the far corner.
And four minutes later, Burnley incredibly scored a 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.
Marcos Alonso's long-range drive was tipped over by Tom Heaton as Chelsea registered their first shot on target early in the second half, while Morata came on to replace the ineffective Michy Batshuayi in attack.
Heaton made an excellent stop from Alonso's curling free-kick, but Chelsea did get a goal back with 21 minutes remaining, Morata swooping in to beat the Burnley keeper with a diving header after Willian's delivery found him in space.
Morata tapped in again soon after, but was denied by an offside flag after converting Christensen's delivery, which may have gone in had the ex-Real Madrid striker left it.
Any chance of a Chelsea recovery appeared to be at an end with nine minutes left as Fabregas – who had been booked for sarcastically applauding a Pawson decision in the first half – received a second yellow for a foul on Cork.
But David Luiz then gave the Blues further hope, rifling a volley past Heaton after racing on to a Morata flick-on.
A frantic finale continued at the other end as Brady hit the woodwork with a set-piece as Burnley ultimately held on through four minutes of added for a famous triumph that piles the pressure on Chelsea after their tumultuous close season.
Key Opta stats:
- Chelsea are only the second reigning Premier League champions to lose the opening game of the following campaign (also Leicester City last season).
- Burnley registered their first opening day victory in the Premier League, after losing each of the previous three.
- Chelsea picked up their first red card in the Premier League in 41 games, since John Terry was dismissed against Sunderland (May 2016).
- Alvaro Morata is the 21st player to score on his Chelsea Premier League debut, and the first since Alexandre Pato in April 2016 (v Aston Villa).
- This is the first time that the reigning champions have suffered a defeat on MD1 in successive top-flight seasons since 1968 (Manchester United 1967-1968 & Manchester City 1968-1969).