The tie was as good as over after Crewe took charge with two goals by Rodney Jack in the space of three first-half minutes, with Vale never looking like getting back into it.
Vale's bright start was blown away as Jack, set up by the outstanding David Vaughan on both occasions, put Crewe firmly in the driving seat. The St Vincent international hammered in an 18yard drive from Vaughn's layoff in the 17th minute, then sprinted onto the youngsters pass to clip in his second.
Crewe then slipped into cruise control for the remainder of the half, giving their hosts a lesson in the art of pass and move football.
Vale made a change at the break, bringing on Ian Armstrong in an attempt to open up a Crewe rearguard well marshalled by Richard Walker. The home side had claims for what looked a blatant penalty refused 18 minutes from time when Armstrong was upended by Efe Sodje right in front of the referee.
But that was just about the only moment of anxiety for Crewe who relied on the counter attack throughout an uneventful second half.
Crewe manager Dario Gradi said: "Rodney and David were the best two players on the field. They were the difference between the sides.
"When you've got two players who sparkle like they did, and everyone else does their job, you will win games."
Vale manager Brian Horton said: "I hate to say it but Crewe were the better side and deserved to go through. They wanted it more and passed the ball very well.
"We have to be a lot more positive at home and our second half performance was very disappointing. The goals killed us and we should have had the character to try to get back at them."