The Brumbies booked a place in the Super Rugby Semi-finals when they escaped a scare by the Cheetahs and held on to win 15-13 in Canberra.
The result means that the Brumbies will travel to Pretoria and face the Bulls in the Semi-final.
The Brumbies have not won in Pretoria since 2006 and have lost their last three matches in the city. They have however won on three of their eight visits.
The Cheetahs outscored the Brumbies by two tries to none and scored their second try a minute from full time.
Riaan Smit had the task of taking the conversion kick from the touchline to level the scores and take the match to extra time.
Ryno Benjamin came on to the field as a late replacement and caught a pass from scrumhalf Sarel Pretorius outside the last defender to score a try that gave the Cheetahs hope of prolonging their best-ever season.
Smit, who had kicked only one of his three previous shots at goal, lined up the conversion from the left-hand touchline and into the teeth of a bitter wind.
His powerful kick sailed towards the posts but, at the last second, drifted away and hit the left-hand post.
In a match in which goalkicks were decisive, Wallabies inside center Christian Leali'ifano shrugged off two early misses to nail four penalties for the Brumbies who will face the Pretoria-based Bulls in next weekend's semifinals.
Leali'ifano missed two of his first three shots at goal, then landed three in succession as the Brumbies relied on penalties to beat the Bloemfontein-based Cheetahs, who were appearing in a playoff match for the first time.
Scrumhalf Nic White also kicked a long-range penalty for the Brumbies, who won the most-recent of their two Super Rugby titles in 2004.
The Christchurch-based Crusaders will now play the Hamilton-based Chiefs, the defending champion, in an all-New Zealand semifinal after their 38-9 win over the Reds on Saturday.
Sunday's match at Canberra didn't come close to matching the high standard set by the seven-time champion Crusaders in their four tries to nil win over the Reds the day before.
The Cheetahs looked stage-struck for the first 15 minutes of the match but came alive when center Johann Sadie scored their first try in the 16th minute, giving them a 5-3 lead.
The lead changed hands three times before White's long-distance penalty in the 47th minute put the Brumbies ahead 9-8.
They then extended that lead to 15-8 with penalties to Leali'ifano in the 58th and 66th minutes.
The Cheetahs refused to let the match get away from them and attacked relentlessly through the last five minutes, remaining competitive though the tide of penalties from New Zealand referee Glen Jackson ran strongly against them.
They had the chance of several kicks at goal in the last five minutes but rejected that option as they sought the converted try that would take the match to extra time.
With time up on the clock at Canberra Stadium, Pretorius engineered the try to Benjamin that gave Smit the chance to tie the scores.
His dying-seconds kick missed by inches and the Cheetahs' longest season, their first that extended to the playoffs, ended in muted disappointment.
Brumbies captain Ben Mowen watched in trepidation as Smit's last kick rose towards the posts.
"You always worry when a South African guy's having a kick at goal because they're usually dead on the money," Mowen said.
"But, fortunately for us, it went our way there."
"I thought there were moments throughout that game when we played some really good footy. "
"We spoke in the dressing room about being enthusiastic, we spoke about out-willing them in those moments and I thought for the majority of the game we did that."
The Brumbies, who topped the Australian conference and finished third overall at the end of the regular season, played a generally conservative and unimaginative match on Sunday.
They kicked for field position and waited for the penalties that inevitably went against the Cheetahs at the fiercely contested breakdown.
"That's an area of strength for us without a doubt, the breakdown," Mowen said.
"That was a good effort but we're going to build now and try to run all the way through.
"We're pretty comfortable with the things we've been working on but we've just got to make sure we execute them under game pressure."
The Cheetahs competed well after their initial hesitation and played some of the match's most attractive rugby.
Their two tries to none advantage might have been enough to win most matches but they were finally denied by missed goalkicks.
Final Score Brumbies 15 (6) Cheetahs 13 (5)
Pen - C.Lealiifano 4, N.White
Tries - J.Sadie, R.Benjamin
Pen - R.Smit
Cards - -
Referee: Glen Jackson (New Zealand)
Assistant Ref 1: Rohan Hoffmann (Australia),
Assistant Ref 2:James Leckie (Australia)
TMO : Matt Goddard (Australia)
1. Scott Sio,2. Stephen Moore,3. Ben Alexander,4. Scott Fardy ,5. Sam Carter,6. Peter Kimlin,7. George Smith,8. Ben Mowen (c),9. Nic White,10. Matt Toomua,11. Clyde Rathbone,12. Christian Lealiifano,13. Tevita Kuridrani,14. Henry Speight,15. Jesse Mogg
Replacements : 16. Siliva Siliva,17. Ruan Smith,18. Fotu Auelua,19. Colby Faingaa,20. Ian Prior,21. Andrew Smith,22. Joe Tomane
15. Hennie Daniller, 14.Willie le Roux, 13.Johann Sadie, 12. Robert Ebersohn (VC) , 11.Raymond Rhule , 10. Riaan Smit, 9. Piet van Zyl, 8. Philip van der Walt, 7.Lappies Labuschagne, 6. Heinrich Brussow, 5. Ligtoring Landman, 4. Lodewyk de Jager, 3. Lourens Adriaanse, 2. Adriaan Strauss (C), 1.Coenie Oosthuizen.
Replacements: 16. Ryno Barnes, 17. Trevor Nyakane, 18.Waltie Vermeulen, 19. Boom Prinsloo, 20.Sarel Pretorius, 21. Elgar Watts, 22.Ryno Benjamin.