Marcelo Bielsa's Whites ensured they left with all three points thanks to Raphinha's first strike for the club 11 minutes from time to settle a game featuring a whole host of chances.
Graham Smyth, the YEP's chief football writer, hands out the scores.
7. Stuart Dallas
8 - Another all-action display. Took responsibility to run Leeds out of pressure. Ran himself into the ground going both ways. Difficult job to mark Rodriguez but stuck to it. Photo by Peter Powell - Pool/Getty Images.
8. Mateusz Klich
8 - Ran and ran all evening long. Clever on the ball, always looked to pass it into space and almost always forward. Should have scored, again.
Photo by Jon Super - Pool/Getty Images.
9. Raphinha
8 - Backed his talent when 25 yards from goal to score a fine effort. Gave Everton real problems with his pace. Played his part defensively, too.
Photo by Clive Brunskill/Getty Images.
10. Jack Harrison
7 - Got in behind Iwobi to good effect and should really have scored at least one goal. Guilty of overplaying once or twice when passes were an option.
Photo by Jon Super - Pool/Getty Images.
11. Patrick Bamford
7 - Frustrated by something when he came off. Some nice hold up play and the usual workrate defensively but will be disappointed with his finishing.
Photo by PETER POWELL/POOL/AFP via Getty Images.
12. Ian Poveda
N/A - Showed lots of confidence to take on two men instead of taking it to the corner and created one last chance. Added energy when it was needed.
Photo by Clive Brunskill/Getty Images.