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.”
13. Mateusz Klich (sub)
7 - Buzzed around. Some clever touches and passes to help unlock a stubborn Crewe block.
14. Patrick Bamford (sub)
9 - An absolute menace. Set up two goals, could have had one or two himself. Changed things completely and ran riot.