Rebels skipper Matt Toomua pulled the strings from inside centre against his old team as flanker Brad Wilkin and hooker Jordan Uelese also crossed to give the exiled Melbourne club a 27-7 lead at halftime.
Seven weeks into a tour that looks set to last the whole season while their home city struggles to contain a second COVID-19 outbreak, the Rebels were unable to cross after the break but still extended their unbeaten run to four matches.
The Brumbies, who scored tries through scrumhalf Joe Powell off their trademark rolling maul and a late effort from Will Miller, never really got into their stride and saw their lead at the top of the standings slashed to four points.
Rebels coach Dave Wessels had made a raft of changes to his team in a bid to get the best of his classy backline.
They paid dividends in the first 16 minutes with fullback Hodge going over in the corner from a slick move and Wilkin crossing after some impressive footballing skills from Australia winger Marika Koroibete.
Reece got his second when Toomua stabbed a neat kick through the defensive line after 23 minutes and the Rebels pack took over to help Uelese across the line just before halftime.
Toomua kicked his second penalty to extend the lead after 53 minutes and that proved the only score in the second half until replacement flanker Miller grabbed a consolation try for the Brumbies in the dying seconds.
The Queensland Reds visit the New South Wales Waratahs in Sydney on Saturday in the other match in round six. (Reporting by Nick Mulvenney, editing by Christian Radnedge)