Jack Harrison opened the scoring after capitalising on a defensive error in a first half which saw the home side look dangerous whenever they won the ball back – which was often as The Clarets kept shooting themselves in the foot.
After the break, half time substitute Maxwel Cornet curled an exceptional free kick into the Leeds to level the scores and set up an exciting final 35 minutes.
Story of the game
Burnley started the game on the front foot with plenty of possession in the attacking areas, but the final ball let The Clarets down.
Junior Firpo then forced Hennessey into a fine save with an inventive flick as Leeds quickly took control.
Hennessey eventually claimed the ball but his distribution was dreadful with the ball eventually dropping to Raphinha who fired his effort over the bar.
Some lovely play through the thirds saw Ayling put in a wonderful delivery for Roberts who put his header wide of the post from inside the six yard box – albeit he was offside.
Leeds soaked up some pressure from Burnley and countered once again with Roberts looking to find Raphinha but it dropped just wide for a goal kick.
The hosts pressure eventually did pay off though through Jack Harrison.
James Tarkowski failed to clear the ball and it fell to Harrison who drove into the box, saw his first effort saved by Hennessey and then converted the rebound at the second time of asking.
Roberts set up Firpo with a lovely, delicate touch but the left back flashed his effort under pressure well over the bar but Leeds continued to look the much better team.
Burnley kept giving the ball away trying to play out of the back with Tarkowski and Ben Mee looking extremely unsettled all through a shocking first half from a Claret perspective.
Before half-time, Wood saw a good chance scooped over the bar after a good chance from Charlie Taylor.
At the break, Marcelo Bielsa would obviously have been much the happier of the two managers but could have been worried about the number of chances they had squandered.
He won a free-kick around the edge of the box and the Ivory Coast international curled a beautiful effort around the wall and right past Meslier to drag The Clarets level.
Ugly scenes marred the celebrations as a fan threw a bottle of fizzy drink towards the celebrating Burnley players, with it hitting Matt Lowton in the face.
The game shot into life as Leeds looked to get back ahead in the game, but neither team looked convincingly like scoring despite a flurry of corners.
Mee seemed to drag substitute Joe Gelhardt down in the area but no penalty was given as the game became quite cagey.
Another Leeds substitute, Daniel James, looked dangerous using his pace to get in behind the Burnley defence, driving a cross across the box to Raphinha who hit the side-netting.
Leeds stayed on the attack and got themselves back in front.
A corner was played square to Stuart Dallas who hit a superb effort into the back of Hennessey’s net with 13 minutes to go.
The hosts looked to control the game and found themselves coming forward through Gelhardt a number of times but Tarkowski got back to win the ball back.
And, as Burnley looked to equalise, Leeds countered once again to wrap up the points through the substitute James.
Mateusz Klich poked the ball through to Gelhardt who fizzed his cross into James who headed it against Hennessey but with so much power that the ball bounced over the line.
On the balance of the game, United much deserved the win in the end as they controlled the game almost from start to finish.
Leeds almost at their best
It was electric from the hosts all game long.
They kept their tails up all game, except for that brief spell after half time when Burnley got back into it.
But they bounced back immediately and were on the front foot and looked dangerous even before scoring their second.
The first half was scintillating and almost the perfect display of counter attacking, which was only lacking the finish on a number of occasions.
The defence stood firm and quickly set Roberts or Raphinha away and they could have had three or four before the break.
The poor finishing could have come back to the haunt them, and possibly will do against a better side that will create chances, so they need to at least hit the target more often to give themselves a chance at scoring.
That team would be a very difficult team to beat when they are fully fit, and will be once Kalvin Phillips and Patrick Bamford are back.
Bamford would have finished at least two of the chances squandered today and Phillips wouldn’t have let Burnley get a sniff back into the game like they did after half time.
In the end, though, an almost perfect day’s work for Leeds United.
It is time to worry about Burnley
They seem to defy criticism for being at the bottom of the league usually, with most saying well what a job they are doing on their shoestring budget.
But that Burnley side would play with heart and desire and with a lot of effort, but this one this season looks defeated before a ball has been kicked.
Aaron Lennon, 34 years old, was the only player who was sprinting back in, getting back to block a cross.
All of them made mistakes at Elland Road, but they didn’t seem to want to fight to make it right.
Tarkowski and Mee are usually so solid and hardly put a foot wrong, and they did make some key interceptions today but their performances were error strewn.
No one raced out to close Dallas down as he shot and, similar to the goals at Old Trafford last time out, no one made an attempt to get to the second ball, Hennessey included.
Wood looked disinterested, McNeil looked a shadow of the player he really is, Tarkowski looked as if he had already left the club.
Even Cornet can not escape criticism today – despite his goal, he waited for the ball far too many times instead of meeting the pass, and that allowed Leeds to break.
That intensity and desire to want to be in possession was the difference.
Next up it is the FA Cup where Leeds face West Ham United before facing them again the week after in the league, while Burnley face Huddersfield Town in the cup before hosting Leicester City a week later.