Whites boss Kevin Blackwell was almost too angry to talk after a shocking first-half performance from the promotion favourites.
A freak eighth minute effort proved to be the only goal of the game, but Crewe could and should have had two or three more in a blistering opening spell.
Steve Jones shot twice at keeper Neil Sullivan, when he was free inside the box but it was the Irish striker's clip across the box that set up the winner.
Veteran defender Gary Kelly lunged to clear and young Jones came up on the blindside to lift the ball over Sullivan into the corner of the net, with the assistance of a deflection off Paul Butler.
Leeds were dismal in the first 45 minutes, struggling to string passes together and Ian Moore wasted their only chance, shooting straight at keeper Ben Williams.
After a half-time roasting, Leeds were camped in the Crewe half but still lacked the quality to break down some sterling resistance from the Cheshire side.
Crewe came close to a second when Michael Higdon flicked on to the far post in a goalmouth melee and Steve Foster's header was scrambled off the line by Sullivan, while Steve Jones should have made the game safe but shot straight at he keeper when he was put through.
The closest Leeds came to levelling was when, with seven minutes left, Danny Pugh's effort was cleared off the line with Frazer Richardson failing to finish off at the far post.