Sportal.co.nz 28.Jul.2013Getty Images
The Bulls - who trailed 11-16 at half-time - looked set to reach the showpiece after they led by four points with just two minutes to play.
But a Matt Toomua pass sent Tevita Kuridrani through the Bulls defence and the latter stormed away to score an excellent try in the 79th minute.
And first five-eighths Christian Lealiifano added the extras as the Australian side notched a stunning road win in the penultimate game of the season.
The Brumbies will now play the Chiefs in the final at the Waikato Stadium on Saturday.
The Brumbies made an excellent start to the match, with Lealiifano kicking the game's first penalty goal after three minutes.
Lealiifano missed another shortly after but Jake White's side jumped to a 10-0 lead thanks to a converted try from Jesse Mogg.
Henry Speight started the move, breaking through the Bulls defence before offloading for Mogg to dive in the corner.
Morne Steyn missed a penalty in response for the Bulls, but they opened their account for the evening in the 15th minute as JJ Engelbrecht powered over.
Steyn provided another unusual miss in the conversion attempt, but he did kick two penalty goals before the break, while Lealiifano also added two more.
Leading by five points at the break, the Brumbies almost surrendered their lead immediately, although Grant Hattingh was held up by Nic White.
Steyn booted two penalty goals in the first 10 minutes of the second half, while Lealiifano kicked one, before the former's fifth of the night edged the Bulls in front for the first time.
They turned down numerous penalties in a bid to score the match-winning try, while a dropped goal attempt also sailed wide, but in the 74th minute, the Bulls - who led by one - won another penalty.
They decided to take the kick on this occasion and Steyn kicked truly, handing the Bulls what looked to be a match-winning lead.
But the visitors had other ideas, as Toomua ran wide before cutting inside and finding Kuridrani.
And he dived over before being mobbed by his team-mates, with Lealiifano putting the finishing touches on an outstanding away win by kicking the resultant conversion.
Scorers were: Bulls 23 (JJ Englebrecht try; Morne Steyn 6 pen) Brumbies 26 (Jesse Mogg, Tevita Kuridrani tries; Christian Lealiifano 2 con, 4 pen). HT: 11-16