Joe Tomane scored a hat-trick of tries as the Brumbies beat the Stormers 39-19 to reach the Super Rugby semi-finals.
The Australian side must now travel to Wellington to face the Hurricanes after sweeping Saturday's last-eight opponents aside at Newlands.
New Zealand-born wing Tomane helped build a 17-3 lead in just 27 minutes of play in Cape Town, meaning the Stormers' spirited attempt to respond following half-time came too late.
After three minutes of frenetic counter-attacking it was the Brumbies who opened the scoring as Tomane found the corner after grabbing a kick from Nic White.
Cristian Lealiifano missed the subsequent conversion, meaning Demetri Catrakilis was able to briefly slash the deficit with a 13th-minute penalty.
The visitors pulled seven points clear a minute later, however, as Tomane got over in the corner for his second try while the Stormers were napping.
Lealiifano was off target again with the boot again but the Brumbies' third try arrived in the 24th minute to offer him a shot at redemption.
Tomane completed a first-half hat-trick as the Australians broke blind following a scrum and t his time, Lealiifano's aim was true.
Catrakilis slotted a penalty on 33 minutes to seemingly keep the Stormers alive, yet their opponents would cross the white line once more before the break.
Scott Sio was the man dotting down on this occasion, the loosehead barging over next to the posts before Lealiifano converted to make it 24-6 at half-time.
The Stormers put their heads together during the interval and returned to the pitch determined to force their way back into the game.
Cheslin Kolbe notched their first try just four minutes after the restart, the full-back intercepting a pass from Matt Toomua and sprinting to touchdown before Catrakilis kicked the extras.
The former Racing Metro trainee then slotted a penalty to make it 24-16 but Lealiifano replied with three more points after the Stormers conceded right under their posts.
Unabashed, Catrakilis scored his fourth penalty of the match, from 40 yards out.
The Brumbies had to go to TMO when Ita Vaea got over just after the hour mark and the Tongan was deemed to have grounded the ball - Lealiifano gladly stepped up to kick the conversion.
There was no such luck for Tomane when he claimed another try in the corner on 66 minutes, as TMO Deon van Blommestein had spotted a high tackle from Jesse Mogg on Dillyn Leyds.
Not even the dismissal of Henry Speight for a dangerous tip tackle on Juan de Jongh could help the Stormers during the final exchanges and, although Lealiifano missed the subsequent conversion, Mogg's last-gasp score was good enough to confirm a convincing 20-point margin of victory.