Town, unbeaten for three months, broke the deadlock when defender Claude Davis rifled them ahead after 22 minutes.
The Jamaican international was on target from 16 yards after a long throw from David Hunt was headed on by Kyle McFadzean.
Tyrone Barnett went close four minutes later by heading a Hunt throw onto the crossbar and the striker later nodded over from eight yards as Crawley dominated possession, while Burton had a let-off shortly after the break when Barnett put a left-footed shot wide from 16 yards.
Crawley doubled their lead after 55 minutes when defender Aaron Webster put through his own goal following a cross from the left by Matt Tubbs, and Tubbs blazed a good chance wide before keeper Ross Atkins parried a goal-bound header from Barnett.
Atkins denied Tubbs twice in quick succession by first stopping a goalbound header and then saving his close-range shot. However, the Red Devils’ top scorer rounded off Crawley’s straightforward win with a tremendous right-footed shot from 30 yards seven minutes from time.