Australia's two-time champions claimed their first winning bonus point of the season to keep on the fringe of the playoffs ahead of a run-in of five tough games.
The Brumbies were never in danger of defeat, reaching halftime with a 21-3 lead and crushing the Cheetahs with six second-half tries for an emphatic victory over the second-last South Africans.
"We were a little scrappy early and we butchered a few scoring opportunities but we were more patient in the second half," Brumbies' skipper Stephen Hoiles said.
"We have some tough opponents ahead and we have to improve to win those games."
The Brumbies have now won 35 of their 37 home games against South African opposition in Super Rugby, while the Cheetahs have lost all their 20 Super 14 matches outside of South Africa.
There was some half-hearted defence from the Bloemfontein-based outfit as the Brumbies ran up a 28-3 lead and secured their four-try bonus point minutes after halftime.
Replacement scrum-half Sarel Pretorius scored the Cheetahs' first try in the 46th minute.
It was a steady procession to the Cheetahs' try-line as the Brumbies posted their biggest win of the season.
But it gets decidedly more difficult for the Brumbies over the next five weeks.
"It was very disappointing tonight," Cheetahs' stand-in skipper Adriaan Strauss said.
"We have a lot of hard work ahead of us and we do need to find some consistency."
Team captain and Springbok flanker Juan Smith returned home and missed the Cheetahs' match after receiving news of his father's death from a heart attack.
The Cheetahs' players wore black armbands in respect for Smith's father.
Source: AFP Global Edition