The Cheetahs outscored the Brumbies by two tries but it was the hosts superior goalkicking that won the day in Canberra.
The Brumbies won 15-13 but Riaan Smit’s 80th minute touchline conversion just failed. A successful kick would have tied the match and taken it into extra time.
The Brumbies, showing greater experience and play-offs composure, dominated the first hour but the last 20 minutes belonged to the Cheetahs and replacement scrumhalf Sarel Pretorius was sensational in providing the impact.
Replacement wing Rayno Benjamin scored from sustained pressure in the 79th minute and Smit, who had kicked just one from three, appeared to have kicked the perfect touchline conversion. But just at the last moment the ball swung to the left of the upright.
The Brumbies now travel to Pretoria to play the Bulls in the semi-final and the Crusaders are away to league winners Chiefs.
Brumbies – Penalties: Christian Lealiifano (4), Nic White.
Cheetahs – Tries: Johann Sadie, Rayno Benjamin. Penalty: Riaan Smit.
Brumbies – 15 Jesse Mogg, 14 Henry Speight, 13 Tevita Kuridrani, 12 Christian Lealiifano, 11 Clyde Rathbone, 10 Matt Toomua, 9 Nic White, 8 Ben Mowen (c), 7 George Smith, 6 Peter Kimlin, 5 Sam Carter, 4 Scott Fardy, 3 Ben Alexander, 2 Stephen Moore, 1 Scott Sio.
Subs: 16 Siliva Siliva, 17 Ruan Smith, 18 Fotu Auelua, 19 Colby Faingaa, 20 Ian Prior, 21 Andrew Smith, 22 Joe Tomane.
Cheetahs – 15 Hennie Daniller, 14 Willie le Roux, 13 Johann Sadie, 12 Robert Ebersohn, 11 Raymond Rhule, 10 Riaan Smit, 9 Piet van Zyl, 8 Philip van der Walt, 7 Lappies Labuschagne, 6 Heinrich Brüssow, 5 Rynhardt Landman, 4 Lodewyk de Jager, 3 Lourens Adriaanse, 2 Adriaan Strauss (c), 1 Coenie Oosthuizen.
Subs: 16 Ryno Barnes, 17 Trevor Nyakane, 18 Waltie Vermeulen, 19 Boom Prinsloo, 20 Sarel Pretorius, 21 Elgar Watts, 22 Rayno Benjamin.