The Whites finally made the breakthrough in the 79th minute as Kalvin Phillips tucked away a Jack Harrison corner, after which Harrison added a brace following stellar work from Patrick Bamford.
Graham Smyth, the YEP's chief football writer, hands out the scores.
Giving his reaction in his post-match press conference, Whites head coach Marcelo Bielsa said: "We took a very long time to score.
"We missed a lot of chances. It was a very contested game. Even if they didn’t create a lot.
"The initial formation they started with, it took us the start of the game to accommodate to it. In both halves we missed 10 chances in each half.”
1. Illan Meslier
7 - Largely untroubled, a spectator for the majority. Made a smart second half stop when called upon.
2. Jamie Shackleton
7 - Struggled to link up with Costa fluently. First half was difficult going forward. Rarely troubled defensively. Got forward more.
3. Diego Llorente
8 - Some terrific passing to help create chances. Produced three that were special. Went off at the break having eased back in comfortably.
4. Pascal Struijk
7 - Solid, in the main. A couple of nervy moments, one in the first half in his own area and one in the second with a Crewe break. Good on the ball for the majority. Picture by Bruce Rollinson.
5. Junior Firpo
8 - Did well. He and Harrison linked up well. He made good runs, was effective in possession and caused problems. Picture by Jonathan Gawthorpe.
6. Kalvin Phillips
8 - Comfortable. Couldn't quite get Leeds playing quickly enough at times but was in control defensively and made the breakthrough.