The after leading 14-3 at half-time.
The Brumbies scored three tries through Connal McInerney and a brace by Folau Fainga'a. Bayley Kuenzle added two conversions with Mackenzie Hansen slotting the match-winning penalty.
The Reds crossed the whitewash twice thanks to Harry Wilson and Angus Scott-Young. James O'Connor added two conversions and two penalties for the visitors.
In next weekend's action, the Brumbies battle the Rebels (Friday, 7 August - 11:05 SA time), while the Reds tackle the Lions in Johannesburg (Saturday, February 8 - 15:05).
Tries: Folau Fainga'a (2), Connal McInerney
Conversions: Bayley Kuenzle (2)
Penalty: Mackenzie Hansen
Tries: Harry Wilson, Angus Scott-Young
Conversions: James O'Connor (2)
Penalties: O'Connor (2)
Substitutes: 16 Connal McInerney, 17 James Slipper, 18 Tom Ross, 19 Tom Cusack, 20 Lachlan McCaffrey, 21 Issak Fines, 22 Mack Hansen, 23 Andy Muirhead
Substitutes: 16 Alex Mafi, 17 Feao Fotuaika, 18 Jack Straker, 19 Ryan Smith, 20 Fraser McReight, 21 Tate McDermott, 22 Bryce Hegarty, 23 Jordan Petaia.
- Compiled by Sport24 staff