The Whites took the lead thanks to a Mateusz Klich strike, and doubled their advantage courtesy of an effort from Jack Harrison just before the hour mark.
Record signing Rodrigo then wrapped up the points late on with a quickfire double, and manager Sean Dyche was not afraid to praise his opponents after the final whistle.
Speaking to the press, he said: "Leeds have been fantastic this season, they are active and fast and work on turnover, and we didn't allow them to do that early in the game, and then the one time we did, we were misshapen and they scored the goal.
"They get their noses in front, and second half we started alright, had a really big chance where their keeper makes a save from Matej Vydra, and then they get sort of a lucky deflection, and it's tough then because we have to open up, which we did.
"We then had another golden chance, and unfortunately they opened us up twice and very very clinical.
"All credit to them for that, we weren't a million miles off, but not as clinical as then."
Next up for Burnley is a clash against Liverpool at Turf Moor on Wednesday evening.
A limited number of supporters will be allowed back inside the ground for the clash, which could have major implications on the Reds’ hopes of securing Champions League football next term.
We’ve gathered the best of today’s Premier League transfer speculation below...
1. PSG after Salah
PSG have already been in touch with Mo Salah’s camp, presumably trying to find out whether the Liverpool player would be interested in a move to France. (L'Equipe) (Photo by Laurence Griffiths/Getty Images)
Photo: Laurence Griffiths
2. Toon want Roberts
Newcastle United are keeping a close eye on Leeds United forward Tyler Roberts ahead of the summer window. (Daily Mail) (Photo by Michael Regan/Getty Images)
Photo: Michael Regan
3. BERLIN, GERMANY - MAY 13: Jadon Sancho of Borussia Dortmund celebrates with the trophy after winning the DFB Cup final match between RB Leipzig and Borussia Dortmund at Olympic Stadium on May 13, 2021 in Berlin, Germany. Sporting stadiums around Germany remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Martin Rose/Getty Images)
Manchester United are in pole position for signing Jadon Sancho and the talks between the Red Devils and the Borussia Dortmund star’s agent are already underway. (Sport1) (Photo by Martin Rose/Getty Images)
Photo: Martin Rose
4. Burnley and Brighton to battle for Man United player
Sunderland have made an offer to Manchester United youngster Jacob Carney with Brighton and Burnley also in the running. (The Sun) (Photo by Catherine Ivill/Getty Images)
Photo: Catherine Ivill