Already trailing to a Stuart Beavon goal, the visitors had goalkeeper Luke Daniels sent off for violent conduct and then fell further behind to Lucas Akins’ penalty.
Burton were on top for much of the first half but failed to test Daniels.
Home debutant Mark Duffy set the tone, blazing wide of an open goal inside three minutes, and Nasser El Khayati was equally wasteful when he ballooned a 10-yard shot on the stroke of half-time.
Burton had an escape when full-back Phil Edwards stabbed Scunthorpe striker Tom Hopper’s low cross against his own post in the 25th minute.
Beavon gave Burton the lead 10 minutes after restart, pouncing on a loose ball and some indifferent defending to drill his shot under Daniels.
The visitors were in deep trouble when Daniels was red-carded after appearing to strike Duffy, with Akins stepping up to double Burton’s lead from the resultant spot kick in the 72nd minute.
Substitute Charlie Goode headed an injury-time consolation goal for the visitors from Gary McSheffrey’s corner.