Losing finalists on two previous occasions, the Waratahs will get the chance to play the competition's deciding game on home soil for the first time, against a Crusaders side that demolished the Sharks 38-6 earlier on Saturday.
Michael Cheika's men led from the third minute at Allianz Stadium following an early runaway try from Alofa Alofa, but the plucky Brumbies hit back to trail by only three points at the break.
The Waratahs' second try also came against the run of play when Kurtley Beale made a one-on-one strip on Jesse Mogg and sprinted 20m to score early in the second half.
From that moment on, the Brumbies piled on the pressure, but their efforts proved in vain as Bernard Foley slotted his third penalty of the night before wrapping up his side's win with a try four minutes from full-time after some brilliant work from Will Skelton.
Skelton beat several Brumbies defenders before throwing a beautiful ball for Foley, who could yet face punishment for a high shot on Nic White earlier in the second half.
Reserve back Taqele Naiyaravoro also faces a nervous wait after he was yellow carded for a shoulder charge on Pat McCabe in the dying moments.
It was a gutsy effort from last year's finalists, who lost star winger Henry Speight to a hamstring injury in the 53rd minute, but the Brumbies' failure to turn pressure into points ultimately cost them.
The Waratahs made a dream start when Alofa swooped on a loose pass from White and sprinted 60m to score the opening try of the contest.
Brumbies full-back Jesse Mogg chased valiantly but Alofa had just enough pace to dive over for an early 5-0 lead.
The hosts stayed on top and increased their lead via a Foley penalty goal in the 22nd minute.
Yet the momentum soon swung and the Brumbies turned down four kickable penalties before their dominance was finally rewarded, Speight cruising over on the short side.
The Waratahs continued to get on the wrong side of referee Jaco Peyper and Christian Lealiifano slotted a simple three-pointer in the 39th minute after the Brumbies were awarded a sixth straight penalty.
However, Foley answered after the siren to put the hosts 11-8 to the good at the break.
Israel Folau was hardly sighted in the first half and put his team under immediate pressure following the restart with a forced offload.
The Brumbies earned another penalty but Lealiifano badly hooked his close-range attempt.
Having been given a let-off, the Waratahs capitalised through Beale before finishing off the gutsy Brumbies in the final 10 minutes.