Calvin Zola's early goal against his former side was enough for Burton to surprise Crewe in the FA Cup.
Zola got ahead of home keeper David Martin to head home Jordan Chapell's cross in the fifth minute.
The Alex were denied by the woodwork three times; Burton's Damien McCrory headed against his own bar, Mathias Pogba hit the post and Ryan Colclough's header came back off the bar.
Lauri Dalla Valle headed inches wide for Crewe as Albion hung on to win.
VIEW FROM THE DRESSING ROOM
Burton Albion manager Gary Rowett told BBC Radio Derby
"Sometimes you have to hold you hands up and look at the opposition and say 'technically, they're probably going to be better than us'.
"So, what we didn't want was lots of space on the pitch for them to exploit and I thought it worked really well.
"We had one or two other opportunities which maybe we could've made more of, but we were really hard to play against and it was another terrific cup performance.
"We've knocked Sheffield United out, we've knocked Leicester City out (both in the Capital One Cup) and now we've knocked Crewe out, so I'm really proud of the players."
Crewe 13 Martin 02 Tootle Booked 03 Davis 05 Ellis Booked 15 Robertson 08 Murphy 19 Osman 26 Aneke (M Clayton - 74' ) 09 Pogba 11 Moore (Colclough - 74' ) 30 Dalla Valle Substitutes 01 Phillips 06 Dugdale 12 Turton 16 Guthrie 31 Inman 07 M Clayton 27 Colclough Burton 16 Lyness 03 Webster 20 O'Connor 21 Holness Booked 08 Weir 11 Palmer (McGrath - 46' ) 14 McCrory 19 Maghoma Booked (Taylor - 81' ) 23 Bell 27 Chapell (Dyer - 75' ) 10 Zola Substitutes 01 Atkins 02 Corbett 06 McGrath 07 Taylor 22 Dyer 09 Richards 29 Kee