The Bulls gave the Hurricanes a big test but fell short, while the Brumbies ensured there will be no South African sides in the last four.
The Brumbies and the Hurricanes recorded contrasting victories on Saturday ahead of home quarter-finals.
Tevita Kuridrani is staying with the Brumbies after re-signing with Rugby Australia until the end of 2020.
The Crusaders ensured they will finish top of the table in Super Rugby after battering the Rebels on Saturday.
The Brumbies have been dealt another blow, with confirmation that Henry Speight will leave the club to join the Reds at the end of 2019.
Australia veteran David Pocock, 31, has played his last game for the Brumbies as he eyes September's Rugby World Cup in Japan.
A 19-13 defeat to the Chiefs has ruined the Reds' hopes of reaching the Super Rugby finals, while the Brumbies beat the Bulls on Friday.
Scott Sio signed a deal with the Wallabies and Brumbies until at least the end of 2022.
Henry Speight scored twice as the Sunwolves were outclassed by the in-form Brumbies at GIO Stadium in Super Rugby.
The Hurricanes scored 26 points in the opening 22 minutes to beat the Rebels, while the Chiefs came back to draw 31-31 with the Highlanders.