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 the perfect start, cutting inside Tony James and curling an angled finish into the after just seven minutes.
Alex doubled their lead in the 19th minute when Donaldson played the perfect pass to Calvin Zola who clipped the ball over the advancing keeper. His shot came back off the foot of a post but Grant was on hand to bang in the rebound.
The Brewers offered little in terms of an attacking threat as Crewe rampaged with front trio Donaldson, Zola and Grant all guilty of missing further chances.
A superb reverse pass from Luke Murphy invited Ashley Westwood to unleash a rasping shot but Albion keeper Artur Krysiak did well to keep it out.
Aaron Webster's free-kick on the stroke half-time almost got the Brewers back in it but Steve Phillips maintained Alex's lead with a fantastic reaction save.
Donaldson continued to run the Brewers ragged after the break and Luke Murphy was unlucky not to apply the finishing touch after the striker picked him out at the far post.
Russell Penn almost gave the visitors a lifeline but his 25-yard piledriver crashed back off the crossbar and Richard Walker's bundled goal at the death was a mere consolation.
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