First half goals from Mateusz Klich and Pablo Hernandez set the Whites on the way to their opening day victory and after Stoke hit back with a penalty a Liam Cooper header made sure the points were United’s.
They survived a few late scares to seal the win, but deserved their success after playing some high tempo football that defied the hot conditions at Elland Road.
Leeds flew out of the blocks in the all action style promised by new head coach Bielsa and could have been ahead in the first five minutes when Kemar Roofe saw his volley parried away by England goalkeeper Jack Butland.
Peter Etebo pulled a shot wide at the other end from the edge of the box while Kalvin Phillips was also off target from range for United.
The opening goal came on 15 minutes when Samuel Saiz went on a good run to the edge of the box and slipped Mateusz Klich in with a clever little through ball. The midfielder did the rest with a calm finish for his first goal in Leeds colours and the Whites were up and running.
They could have been two up shortly after as Saiz saw a goalbound strike well blocked by a Stoke defender.
The visitors had a better spell with their new signing, Tom Ince hitting the woodwork with a shot from the edge of the box and Etebo seeing a shot saved low down by home keeper Bailey Peacok-Farrell.
Leeds produced a strong finish to the half, however, with three chances in three minutes as Ezgjan Alioski’s volley was saved by Butland, Roofe’s shot rolled just the wrong side of the post and Alioski headed wide.
They doubled their advantage right at the end of the half when Pablo Hernandez was put through by Alioski and his shot could not be kept out by Butland who got down to save only to see the ball go in off the post.
Stoke pulled a goal back early in the second half as they awarded a penalty as Ince went down under a challenge from Barry Douglas and Benik Afobe stepped up to score from the spot.
Leeds did not lose confidence, however, as they won a corner and scored a third goal with Cooper heading home Douglas’s corner.
Klich sent a volley wide as the Whites went for more goals before the visitors put in their bigger finish after sending on Peter Crouch up front.
James McClean’s free-kick was saved at full stretch by Peacock-Farrell and the follow-up cross was headed onto the top of the net by Bruno Martins Indi.
Peacock-Farrell was called into action again to keep out a Crouch header after the tall striker had pulled to the far post.
In injury-time Joe Allen’s close range effort was cleared off the line, but United saw out five minutes of injury-time to seal their victory.
Coach Bielsa was obviously happy with the winning opening to the season, but thought the team could improve.
He said: “It was a game with high intensity. Our players were ambitious and they did a great physical effort.
“In some ways we played as we wanted, but in some instances we gave the ball to the other team and we would have done better.
“The physical effort of the players and the productivity was pretty high. Our offensive actions were very good in some moments.
“My team took risks when they had the ball and this was positive. But we lacked a bit of experience at the end of the game.
“Our team has to improve and get better. At the end of the game our team did not link defence and attack on the ground and we did not move the ball as well as we could. They are all parts of the game we can improve.
On the reception to himself and the team from the fans in a 34,126 crowd, Bielsa added: “It was even bigger than I expected. The fans were connected to the messages of the team in every second of the game.
“I would like to thank the fans for their support and I hope our football will create positive reaction from the fans.”
Stoke manager Gary Rowett was impressed by Leeds.
He said: “Leeds played very, very well. I thought we made it too easy for them, but you could see their movement was better than last season.
“They looked very well organised and the Elland Road crowd played its part as it always does.”
Leeds United 3
(Klich 15, Hernandez 45+1, Cooper 57)
Stoke City 1
(Afobe 52, pen)
Sunday, August 5, 2018
Sky Bet Championship
Leeds: Peacock-Farrell, Ayling, Berardi, Cooper, Douglas, Phillips, Klich (Dallas 76), Hernandez, Saiz (Baker 88), Alioski (Harrison 89), Roofe.
Stoke: Butland, Bauer, Shawcross, Martins Indi, Pieters, Badou (Fletcher 62), Etebo (Bojan 62), Allen, Ince, McClean, Afobe (Crouch 76).
Referee: Scott Duncan.