First-half goals from Clayton Donaldson and Joel Grant sank Burton as Crewe ended their five-game winless streak at home.
Donaldson got Crewe off to a great start as he cut inside Tony James and curled the ball in the net after seven minutes.
Alex doubled their lead in the 19th minute when Donaldson passed to Calvin Zola who clipped the ball over Artur Krysiak.
The Brewers offered little in terms of an attacking threat as Crewe dominated with their front trio.
Aaron Webster’s free-kick on the stroke half-time almost got the Brewers back in it, but Crewe’s keeper, Steve Phillips maintained their lead with a fantastic save.
Donaldson continued to run the Brewers ragged after the break and Luke Murphy was unlucky not to apply the finishing touch.
Russell Penn almost gave the visitors a lifeline but his 25-yard piledriver crashed back off the crossbar and Richard Walker’s bundled goal in extra time was a mere consolation.
crew are a good side , they are hard to beat at home .