The signs of a bad afternoon for Chelsea came when captain, Gary Cahill, got a straight red card in the 14th minute.
Any hopes of an unlikely comeback looked to have disappeared when midfielder Cesc Fabregas was red-carded in the 81st after receiving his second booking.
Chelsea had not lost on the opening day of the season since 1998 and paraded the Premier League trophy before kick-off as a reminder of the size of the task facing the Clarets.
Antonio Conte was without Eden Hazard, Pedro Rodriguez and Victor Moses for the encuonter.
It is not since March 2014 that Chelsea have had two players sent off in the same game in the Premier League and only the seventh occasion on which it has happened in their Premier League history.
Chelsea are expected to make new signings before the end of the transfer window with British media reporting that Conte is dissatisfied with the depth of his squad. We kept a good shape early in the game, but the sending off makes a big difference.
Six minutes before half-time, left-back Stephen Ward made it 2-0 in stunning fashion.
Striker Jay Rodriguez, bought from Southampton during the summer for £12 million (NZ$21.3 million), was busy early on for the home side, going close twice in two first-half minutes with a header and a shot.
Kick-off is just under a half hour from now. He scored off a Willian assist and then helped David Luiz to a goal with five minutes to play.
It's off to a disastrous start at Stamford Bridge as the Blues are now losing to lower table side Burnley at home.
Burnley had to wait until their penultimate away game to win on the road last season, and Dyche smiled: "Three years ago, it was a story getting a win, the away win was a story last year, and it kills all that off".
Chelsea are the league's best team when it comes to opening the season.