The victory is only the Cheetahs’ third of the season, but sees them move up to 12th spot on the overall log with the Stormers, Lions and Reds trailing.
The Cheetahs started well, particularly after another loss against the Western Force last weekend in Bloemfontein.
They put the Brumbies under pressure early on and as a result, flyhalf Johan Goosen kicked a penalty to put his side in the lead.
The Brumbies almost got on the board, but a seemingly well constructed backline move saw obstruction come into play and the five pointer was squashed.
Goosen launched a monster of a kick and from the line-out, kicked another penalty as the Brumbies played the man in the air.
Brumbies centre Christian Leali’ifano got his first shot at goal in the 10th minute, as the Cheetahs infringed at the breakdown, but his first attempt of the evening went wide and the hosts retained their lead of six points.
Ill-discipline by the Brumbies on the defence led to an early team warning for the visitors and lock Scott Fardy was yellow-carded in the 16th minute after the Canberra-based side kept infringing.
Goosen kicked his third penalty of the evening, stretching the hosts’ lead to nine points.
Leali’ifano missed with his second attempt in the 19th minute, letting the Cheetahs of the hook as the hosts were pinned for obstruction.
Leali’ifano’s misfortune with his kicking boot meant the ball was handed to scrumhalf Nick White, who finally put his side on the scoreboard in the 21st minute.
That sparked the Brumbies to attack more and winger Robbie Coleman dotted down in the corner after a clever little box-kick by White.
The latter, however, could not convert the try, leaving the visitors to trail by a single point seven minutes from half-time.
White slotted his second penalty on the hooter to put his side in the lead at the break.
The second half started slowly, but the Cheetahs regained their lead in the 47th minute after good attacking play led to a try for Springbok playmaker Willie le Roux.
Goosen missed with the conversion, but the hosts again enjoyed a lead of four points.
Goosen scored the Cheetahs’ second try of the evening after a clever cross-kick by replacement Elgar Watts.
Goosen picked the ball out of the air and dotted down in the corner in the 50th minute.
Goosen converted his own try to stretch the lead to ten points for the hosts.
With little more than 20 minutes left, Goosen kicked another penalty to increase their advantage, but White cancelled it out with his third successful attempt of the evening.
Cheetahs flanker Heinrich Brussow was sin-binned in the last ten minutes for kicking the ball away after a penalty and the Brumbies used that to get their second try, courtesy of hooker Stephen Moore.
White converted to reduce the deficit to just three points.
Goosen had the last say when he slotted a drop goal in the dying minutes to secure the victory for the Bloemfontein outfit.
Scorers: Cheetahs 27 (9): Tries: Wille le Roux, Johan Goosen. Conversion: Johan Goosen. Penalties: Johan Goosen (4). Drop goal: Johan Goosen.
Brumbies 21 (11): Tries: Robbie Coleman, Stephen Moore. Conversion: Nick White. Penalties: Nick White (3).