Luke Murphy's strike proved decisive as Crewe saw off Burton.
Danny Shelley drove home a low strike to give the hosts the lead before teeing up Ashley Westwood to rifle a fierce shot into the roof of the net.
Callum Driver pulled one back for the Brewers with a smart finish after latching onto Adam Bolder's through ball, only for Murphy to extend the advantage from close range.
Calvin Zola scored from a narrow angle in stoppage time but it was not enough.
VIEWS FROM THE DRESSING ROOM
Crewe manager Steve Davis told BBC Radio Stoke:
"We've had a lot of goals in the last three home games, but as long as we're getting the three points, I'm not bothered if it's 5-4 or 6-5.
"It's a big win with us being under strength. We were short and we knew that because we had a very young bench.
"There were a lot of adjustments and a lot of things that we had to change very quickly.
"It was a battling performance under the circumstances so it makes it a very good win tonight."