Clayton Donaldson came off the bench to grab a late winner as Burton surrendered their five-game unbeaten run in a 2-1 home defeat.
The striker grabbed his sixth goal of the season in the 84th minute to give Alex the double over the League Two new boys.
The game was delayed for 15 minutes after referee Steve Bratt suffered an injury in the warm-up, but it came to life with two goals in as many minutes midway through the first half.
Crewe made the brighter start and were rewarded in the 27th minute when Shaun Miller expertly steered home an angled shot from 12 yards after seizing on a Luke Murphy pass.
The visitors' joy was short-lived, however, as Burton skipper John McGrath fed the ball through for Shaun Harrad to lash home his 12th goal of the season from 15 yards.
Burton piled forward after the interval, with Harrad hitting a post and then forcing Alex goalkeeper Steve Phillips to make another important save - but it was Alex who stole the points when Donaldson pounced on Byron Moore's low cross.
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