Christian Leali'ifano and lock Blake Enever scored the tries for the Brumbies, who should have added more but for their own errors on the Cheetahs' line and some scrambling defence by the Bloemfontein-based outfit.
“We got over the line a few times... but that's the way it goes. We are happy with the win,” Brumbies skipper Stephen Moore said in a pitchside interview.
Leali'ifano also added 10 points with the boot to keep the Brumbies top of the Australian Conference following their fifth win of the campaign.
The inside centre needed just three minutes to wriggle through for the first try after some poor Cheetahs tackling but the hosts were guilty of butchering other scoring attempts with Henry Speight and Matt Toomua denied on the line.
Leali'ifano converted his try and added two penalties to one from Joe Pietersen to send the Brumbies in 13-3 at the break.
The second period started in similar fashion to the first with the Brumbies driving towards the Cheetahs' line before lock Enever dived over in the 44th minute for his first try in Super Rugby as the ensuing conversion completed the scoring.
For the Cheetahs, it was a fifth straight loss and they now travel to Perth to take on the Western Force next week hoping to end their four-week Australasian tour on a high.
Original source: Brumbies bulldoze over Cheetahs