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The Australian conference-winning Tahs will host the Highlanders in a knockout quarter-final next weekend, but the Rebels (ninth) and Brumbies (tenth) both fell just short.
The Victorian franchise was edged out of a final eight spot on points differential by South Africa's Sharks, who scored a 20-10 home win over Argentina's Jaguares in the last match of the regular season on Sunday ( AEST).
Both the Sharks and the Rebels, who lost 43-37 to the Highlanders in Dunedin on Saturday, finished on 36 points.
Each finished level on wins, the initial tie-breaker, but the Sharks had a -5 points differential to the Rebels -21.
The Sharks will play away to overall ladder leader and New Zealand conference winners the Crusaders, the defending champions.
The Brumbies finished two points off eighth spot after a rousing final-round 40-31 away win over the Waratahs in Sydney on Saturday night.
The Lions, the losing finalist for the last two seasons, will host the Jaguares after clinching top spot in the South African conference with a 38-12 home win over the Bulls early Sunday (AEST).
The other quarter-final will be an all New Zealand battle - the Hurricanes hosting the Chiefs.
The Tahs dropped to third on the overall ladder after losing to the Brumbies on Saturday, with the Lions later replacing them in second spot.
The match between the Tahs and the sixth-placed Highlanders, who they beat 41-12 in Sydney back in May, is expected to be played next Saturday, with the details to be confirmed later today.
The Tahs conceded six tries to the Brumbies, whose own slim playoff hopes ended when the Rebels picked up a bonus-point in Dunedin.
How the quarterfinals will play out:
Friday, July 20
Hurricanes v Chiefs - Westpac Stadium, Wellington at 7.35pm
Saturday, July 21
Crusaders v Sharks - AMI Stadium, Christchurch at 7.35pm
Waratahs v Highlanders - Allianz Stadium, Sydney at 8.05pm
Lions v Jaguares - Emirates Airline Park, Johannesburg 3:05pm
(All times are local time)