The home side were put under pressure early on at Eden Park, as the Brumbies' second-five Irae Simone silenced the home crowd with a barnstorming try in just the third minute of the game.
After a perfect start by the Brumbies the Blues quickly took control of the game, playing open running rugby which ultimately led to their first try of the game through number-eight Hoskins Sotutu.
The home side continued to dominate the game in the first-half, with first-five Beauden Barrett orchestrating much of the play.
The Blues' showcased their flair and improvisation in amazing move which set up Mark Telea to score the home side's second try, giving themselves momentum going into the second half with a 20-7 lead.
However, the second half played out as a tense affair with both teams unable to put points on the board for much of the half.
The Brumbies eventually hit back with a vital try through substitute hooker Lachlan Lonergan, shortly after the Blues' had their own hooker Kurt Eklund yellow carded for a dangerous tackle.
With the Australian side on the hunt for a comeback, the Blues were forced to put in a huge amount of work at the set piece to disrupt the Brumbies' desperate attacks.
The Brumbies were given a boost when the Blues lost another player to the sin bin with flanker Adrian Choat receiving a yellow card for a dangerous tackle.
Shortly after, the Brumbies scored their third try through Lachlan Lonergan who once again dotted down off the back of a rolling maul, cutting the Blues' lead to just one point at 20-19.
The closing minutes were extremely tense, with Ofa Tu'angafasi forced to dramatically charge down a late drop goal attempt by the Brumbies.
"They are a quality outfit the Brumbies. We knew they would go to the full 80 and they didn't disappoint," said Blues skipper Beauden Barrett.
"We're excited to be back here next week. We've given ourselves a chance and that's all we can ask for."
The Blues' win means they will meet the Crusaders in a home final at Eden Park next Saturday.
Photo: Photosport Caption: Beauden Barrett of the Blues breaks a tackle against the Brumbies.