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But victory came at a cost, with goalkicking fullback Mark Gerrard limping off in the closing stages with a leg injury.
The Brumbies already have Wallabies stars Stirling Mortlock, Adam Ashley-Cooper and Clyde Rathbone on the sidelines, plus the career-ending brain tumour to Julian Huxley.
Now Gerrard is tipped to miss at least two games, further depleting the Brumbies backline.
With the bye next week, Brumbies coach Laurie Fisher said beating the winless Cheetahs was "non-negotiable" tonight but the match was in the balance until midway through the second half.
A Gerrard penalty goal in the 53rd minute nudged the Brumbies ahead 15-13 before centre Tyrone Smith displayed some brilliant footwork to beat five defenders and cross six minutes later.
Gerrard's conversion gave the Brumbies some breathing space at 22-13 and lock Mitchell Chapman relieved all pressure when he took a great one-handed pass from Julian Salvi to score his side's fourth try in the 64th minute.
The Cheetahs rallied to secure a bonus point themselves with a try to replacement halfback Tewis de Bruyn and a penalty after the bell to Jacques-Louis Potgieter to close the gap to less than seven points.
A penalty goal on the stroke of halftime to flyhalf Conrad Barnard nudged the South Africans in front by a point, despite the home team posting two tries to one in the first 40 minutes.
Barnard opened the scoring with a penalty in the eighth minute before Brumbies lock Mark Chisholm broke the Cheetahs' defence and showed great pace to run 30 metres and score in the left corner five minutes later.
Gerrard's conversion gave the Brumbies a 7-3 lead, only for the Cheetahs to regain the advantage with a fine try to winger Jongi Nokwe in the 23rd minute.
Barnard added the extras to make it 10-7 before the Brumbies struck back in the 32nd minute after some intelligent play from halfback Josh Holmes.
From a penalty 10 metres out from the Cheetahs line, Holmes took a quick tap and spread the ball wide and some good hands from No.8 Stephen Hoiles put winger Peter Playford over in the right-hand corner.
The Brumbies were ahead again, but Barnard had the final say of the half as the last-placed Cheetahs set their sights on their first win of the season.
Alas, it was not to be as the Brumbies lifted their game in the second stanza.
Brumbies29: ( Mark Chisholm , Peter Playford, Tyrone Smith, Mitchell Chapman tries; Mark Gerrard 1 pen, 3 con)
Cheetahs 23: (Jongi Nokwe, M de Bruyn try; Conrad Barnard 2 pen, 1 con; J-L Potgieter 1 pen, 1 con).Halftime: 12-13.
