The victory ensured the Brumbies' third title at Super Rugby level, having won the broader international Super Rugby competition in 2001 and 2004.
Hooker Folau Fainga'a, winger Andy Muirhead and fullback Tom Banks all crossed for the home side, while first-five Noah Lolesio, surprisingly brought back after two months out with a hamstring injury, kicked 13 points.
Loose forward Harry Wilson and lock Angus Blyth scored tries for the Reds and James O'Connor added 13 points from the boot to give them hopes of adding to their only Super Rugby title in 2011.
"It was a huge effort from the boys," Brumbies captain Allan Alaalatoa said. "We always knew the Reds were going to come back in the second half.
"We did really well to close out that game."
The Brumbies played to their traditional strength, turning around the Reds with tactical kicking, superb ball retention and putting pressure on them in their own half.
They also took advantage of some poor discipline to establish a 15-3 lead with tries to Fainga'a and Muirhead.