Evans produced a rare moment of quality eight minutes from time to settle a frantic game at the B2net Stadium.
Chesterfield had failed to keep a clean sheet in their previous 13 games but they defended well in the first half and Greg Fleming twice saved well from Evans and Chris Porter.
Steve Simonsen denied Lee Johnson just before half time and Fleming again saved from Evans before Leon Clarke struck the United bar with an overhead kick in the 62nd minute.
The game appeared to be heading for stalemate when Evans picked the ball up 30 yards from goals and slipped past two defenders before firing low into the bottom right corner from 15 yards.
Chesterfield responded with a triple substitution but Stephen Quinn almost added a second before 2,000 United fans celebrated a first away League win since October.
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