Sam Vokes scored twice and Stephen Ward struck a goal for the ages as the Clarets made the dream start to their Premier League campaign in a Stamford Bridge thriller.
Vokes picked up where he left off as last season’s leading scorer with goals either side of a Ward thunderbolt - after Gary Cahill had been sent off for an early foul on Steven Defour - to give Sean Dyche’s men a remarkable 3-0 half-time lead.
And they needed all of that cushion to survive a second half fightback from the champions – who finished with nine men after Cesc Fabregas’ late dismissal for a second yellow card.
Substitute Alvaro Morata and David Luiz pulled goals back to leave Burnley hanging on.
But they did so in heroic fashion to banish the memories of last season's long wait for a solitary away success to register an immediate and magnificicent win on the road and lay down a marker for the battles to come.
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.
But Burnley went in unbowed as they chased their first top-flight win on the first day of a campaign since 1973.
And they were given a helping hand after 14 minutes was Cahill was dismissed.
Marcos Alonso had seen yellow for a high and late challenge on Matthew Lowton in the opening exchanges.
And when Cahill over-ran the ball and lunged towards Defour in an effort to win it back, referee Craig Pawson decided this time it warranted an early bath for the Clarets’ one-time player of the year.
Burnley – starting with a 4-4-1-1 formation - had held their own up to that point with James Tarkowski superbly filling the boots vacated by Michael Keane at the centre of the Clarets’ defence.
And facing 10-men, Dyche’s men then seized the initiative to score three times in a glorious 20-minute spell.
Vokes got the all-important first, hooking in a cross from Lowton to continue the purple patch he had harvested at the end of last season.
Ward then made it 2-0 with a stunning strike, crashing home an angled volley after playing a one-two with Chelsea old boy Jack Cork.
And the Clarets’ joy was unconfined when Vokes made it three, two minutes before the break.
Again it was a wonderful goal which demonstrated the belief running through the Clarets’ ranks.
Robbie Brady played a short free-kick to Steve Defour, who superbly picked out Vokes to score with a thumping header and make it seven goals in his last six club games – the first Burnley player to score in four successive Premier League matches.
Tom Heaton had barely been troubled behind Burnley’s resolute wall of claret and white but four minutes into the second half the captain stepped up, touching over a piledriver from Alonso as the wounded champions tried to muster a response.
Invevitably, the home side generated a period of pressure as the Clarets looked to keep a vice-like grip on their advantage by defending deep when necessary.
And with Chelsea struggling to find a way through, manager Antonio Conte sent on £60m man Morata for his debut following summer move from Real Madrid to try and spark a fightback.
Again it was Alonso who carried the next threat with a long-range free-kick which was superbly tipped over the top by Heaton.
But Morata didn’t need long to make his mark as he pulled one back with 22 minutes to go as the Blues finally made their possession count, Willian crossing for Morata to get in behind Burnley’s back line and glance home a diving header.
Willian was becoming an increasingly pivotal figure, pulling the strings around the edge of the Clarets’ penalty area and Burnley survived another scare when then midfielder picked out Andreas Christensen for an effort ruled out as Morata touched the ball home from an off-side position.
It was fevered stuff in a cauldron-like atmosphere – Fabregas collecting a second yellow card for a foul on Cork eight minutes from the end - as the Clarets battled to hold out for a famous win.
Luiz made it a nerve-shredding end as raced through to pull another goal back for the nine men, drilling the ball home from Morata’s flick-on.
Brady then hit a post with a 90th-minute free-kick as he was only inches away from giving the Clarets desperately needed breathing space.
With four minutes of injury time added on it was near purgatory but the Clarets heroically saw it through to secure a first success at Stamford Bridge since 1971.
It was worth the wait.
Burnley: Heaton, Lowton, Tarkowski, Mee, Ward, Gudmundsson (Arfield 74), Defour (Walters 74), Cork, Brady, Hendrick, Vokes. Substitutes: Pope, Long, Taylor, Westwood, Barnes.
Booked: Brady, Mee, Arfield.
Chelsea: Courtois, Rudiger, Azpilicueta, Luiz, Cahill, Alonso, Kante, Fabregas, Boga (Christensen 18 (Musonda 90+1)), Batshuayi (Morata 58), Willian. Substitutes: Caballero, Kenedy, Musondra, Tomori, Scott.
Booked: Alonso, Fabregas, Rudiger, Luiz.
Sent off: Cahill 15, Fabreags 82
Referee: Craig Pawson