With the man advantage, Burnley took the lead on 24 minutes.
New boy Alvaro Morata got a second half goal back before David Luiz's late goal gave the Chelsea faithful a glimmer of hope of a sensational comeback.But Cesc Fabregas was then sent off for a second yellow with eight minutes left.
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.
The result will not improve the mood of Chelsea manager Antonio Conte, who hasn't hidden his frustration at failing to significantly bolster his squad in the offseason.
Conte, in an interview with the BBC after their 3-2 loss to Burnley on Saturday, stated that he was focused on working with the players at his disposal.
Jeremie Boga, on his league debut was sacrificed in favour of substitute centre-back Andreas Christensen, also making his league, debut on 18 minutes.
"It was a pity because our fight in the second half was very good", Conte said.
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.
"It's hard at this club to make massive strides, it's about shifting it forward, and this won't do us any harm at all".
It is only one game, yet the parallels with Chelsea's last defence of a Premier League title two seasons ago under Jose Mourinho were uncanny.
Conte is desperate for reinforcements in the final three weeks of the transfer window. Chelsea's new club captain was dismissed for a clumsy challenge on Defour early in this contest. "I think that the coach can make mistakes, the players can make mistakes, the referee [too]".
Burnley was expected to struggle this season after losing arguably its best two players in the offseason, defender Michael Keane and striker Andre Gray.