Crawley dominated much of the game but could not break down a determined Albion defence.
Gary Alexander and Scott Davies both went close in the first five minutes and goalkeeper Ross Atkins twice had to come to the rescue of the hosts, tipping over shots from Hope Akpan and Davies.
On the rare occasions when Burton did get forward, Crawley keeper Michel Kuipers comfortably dealt with efforts from Jimmy Phillips and Jacques Maghoma.
The pattern of the game remained unaltered after the break but a wayward Dannie Bulman shot was all the visitors had to show for another wave of heavy pressure.
The Red Devils thought they should have had a penalty for a handling offence by Nathan Stanton in the 77th minute, but referee Roger East brushed aside their protests.
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