The home team dominated much of the game, especially in the first half, but they were wasteful up front.
They missed the target with half-a-dozen first-half chances and Richie Humphreys powered a header against the post just before the break.
With Gary Liddle missing a sitter just after half-time, it looked like being the same story in the second half as a hard-working Crewe battled to stay in the game.
But they suddenly came to life in the last quarter, inspired by the breakthrough goal from defender Michael Nelson on 67 minutes.
He came forward for a corner and when it was taken short for Robbie Elliott to cross from the left, Nelson was at the far post to power his header into the roof of the net.
Crewe had looked dangerous on occasional breaks and they still did, but they were killed off in the last five minutes by two goals from home sub Richard Barker.
On 85 minutes he slotted in easily after a good run on the right and a cut-back from the goal-line by the outstanding Ian Moore.
And Barker scored from the spot a minute later after Moore had been chopped down in the area by Michael O'Connor.
Crewe could possibly claim they didn't deserve to lose by such a big scoreline, but they had been outplayed in the first half and the score could have been 3-0 or more at half-time with better finishing from the home forwards.