Steyn kicked a penalty when the Bulls were awarded a fourth late chance but the lead was not enough as the Brumbies claimed a converted try to centre Tevita Kuridrani with 90 seconds left to win 26-23.
The fate of the Super 15 semifinal lay with a decision from South African TMO Shaun Veldsman as the Loftus crowd roared their disgust. Veldsman gave the backline move a green light and the Brumbies were into the final. It continues their ascendant season under the command of former Springbok coach Jake White, who has helped transform the squad into a group with strong plans and an unbending spine.
They lost captain David Pocock and midfield back Pat McCabe but have wrung a great deal from the group.
George Smith has made a stunning return to his old team after White asked for help from the veteran.
The 33-year-old flanker was immense in the semifinal, pinching breakdown ball, slamming Bulls players in contact and shrugging them aside with his carries.
Smith's grappling effort to hold up Bulls lock Grant Hattingh over the line was a superb example of the flanker's influence and his duel with Tanerau Latimer, Sam Cane, Liam Messam and co on Saturday night will be huge.
Five-eighths Matt Toomua is another who is firing for the Brumbies. Toomua kicks and runs strongly and it was his late blindside snipe past a tiring forward and an over-eager Francois Hougaard, which created the winning try for Veldsman.
Tackling is one of Toomua's strengths and unlike other five-eighths in Australia, he defends up in the line which gives the Brumbies better definition.
Victory for the Brumbies means they are going to the final for the first time in nine years. It was a time, captain Ben Mowen said, for them to "write new stories".