Luca Koleosho scored a stunning first-half breakaway goal as Burnley destroyed Leeds' unbeaten start to the season in front of Hollywood actor Will Ferrell.
Scott Parker's Clarets struck in the 18th minute when Leeds winger Manor Solomon, on loan from Tottenham, slipped and lost the ball inside his own half.
Winger Koleosho, 19, collected possession and raced into the hosts' 18-yard box unopposed before firing a superb low, right-foot shot into the bottom corner of Illan Meslier's net.
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Leeds had chances during the first half - striker Mateo Joseph fired wide when clean through inside the opening minute - but they could no way through a resolute Burnley rearguard with goalkeeper James Trafford in fine form.
The visitors lost defender Bashir Humphreys to a second yellow card in the closing stages as the visitors held on for a huge win.
At a packed Elland Road, Ferrell watched on from the directors' box in the West Yorkshire sunshine, having come on board as an investor in Leeds earlier this year.
The 57-year-old Anchorman star is one of many high-profile personalities, including athletes, who have made investments in the Whites through 49ers Enterprises.
But he was left disappointed as Daniel Farke's men tasted defeat in the league for the first time this season as the Clarets displayed their own promotion credentials.
Leeds were unchanged from the side which beat Hull 2-0 at home before the international break and there was a pre-match minute's applause for former Whites captain Sol Bamba following his recent death.
But Joseph spurned an immediate golden opportunity to put the hosts ahead.
He dispossessed Burnley defender Maxime Esteve on halfway and raced into the 18-yard box before side-footing a low, right-foot shot wide of Trafford's post.
It was a huge chance wasted and the Clarets soon showed their threat at the other end when Josh Laurent crossed from the left flank and Hannibal headed wide.
The game was briefly halted as Elland Road rose in the sixth minute to applaud Leeds fan Bob who died at the age of six earlier this month.
In the 18th minute, Burnley led as Koleosho found the net in stunning fashion after Solomon slipped inside his own half, gifting possession to Koleosho.
He broke clear down the right flank and strode unchallenged into the hosts' 18-yard box before hitting a low, right-footed shot into the left-hand corner of the net.
The defending from Leeds was awful, with Koleosho allowed to run around 50 yards unchecked before shooting past Meslier.
It was the first goal Leeds had conceded in the league since the opening day, but the scores were almost level in the 23rd minute.
USA midfielder Brenden Aaronson played a teasing ball behind the Burnley defence to find Willy Gnonto, who broke the offside trap.
The Italy forward hit a first-time shot with his left foot from the edge of the six-yard box but Trafford made a superb save to thwart him.
Moments later, the Clarets ventured upfield and former Leeds loanee Jaidon Anthony cut inside Jayden Bogle before firing just wide of the far post.
Nine minutes before the break, Leeds appealed for a penalty when Solomon hit the turf under a challenge from Joe Worrall but referee James Bell was unmoved.
After an entertaining first half, Leeds went close to an equaliser in the 52nd minute when Joseph curled a right-foot shot from the edge of the 18-yard box which Trafford turned around a post.
Eleven minutes later, Whites captain Ethan Ampadu hit a dipping right-foot shot from 20 yards which Trafford tipped over the crossbar.
Chances grew scarce as the match wore on while Rodon and Burnley captain Josh Brownhill both required treatment following a nasty clash of heads.
Burnley then lost Humphreys to a second yellow in the eighth and final minute of added time but Leeds could find no way through.
The managers
Leeds' Daniel Farke:
"It's the most frustrating thing in football when you go back to the dressing room and you can't explain how you didn't win this game.
"If I'm honest, after the international break I didn't expect us to be as dominant as we were today.
"I'm really happy with our dominance and how we started the game but, being self-critical, in the decisive moments we weren't effective enough.
"We should have scored in the first two minutes and we should have had a penalty as well.
"Credit to Burnley - although they had an 85-yard sprint, it was a really good finish into the bottom corner.
"We had the better and easier chances but we didn't take them and this is where we have to be self-critical.
"It was also disappointing to concede out of such a situation but to dominate a good side like Burnley, I was pleased with the way we played.
"But obviously we're not happy with our effectiveness and this is why we lost."
Burnley's Scott Parker:
"It's a massive three points for us, especially at such a tough place to come and where we are in the stages of our development as well.
"The foundation that got us the result was everything we stand for as a team - grit, determination and battling spirit to a man.
"We showed every bit of that, which was the reason we got the three points, and it was a brilliant finish from Luca.
"Not many players can run 60 or 70 yards up the pitch at full pace with the calmness Luca showed to execute the finish.
"I'm delighted for him and thought he was brilliant in his moments today."