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The Hurricanes, Jaguares and Brumbies all claimed wins at home to join the Crusaders in next week's semifinals.
That guarantees one New Zealand team in the final - the Crusaders and Hurricanes facing off in Christchurch on Saturday.
In the other semifinal the Jaguares host the Brumbies on Saturday morning.
The Hurricanes had to withstand a strong challenge from the Bulls, but emerged 35-28 victors in Wellington.
After trailing 7-3 early, the hosts hit back with three consecutive tries to TJ Perenara, Ben Lam and Salesi Rayasi to put themselves in a dominant position at 24-7.
Cornal Hendricks got one back before the break for the Bulls, but Rayasi grabbed a second to make it 29-14.
Rayasi then blotted his copybook when he was ruled to have deliberately knocked down a Bulls pass while they were on attack.
Referee Nic Berry awarded a penalty try and sent him to the sin-bin.
Hendricks scored again while Rayasi was off the field and made it 32-28.
But the boot of Jordie Barrett helped the Hurricanes close out the win.
Meanwhile, a superb defensive effort helped the Jaguares to a 21-16 win over the Chiefs in Buenos Aires.
The Jaguares kept the New Zealand side scoreless in the final 30 minutes to set up a home semifinal.
Flanker Pablo Matera and winger Matias Moroni scored tries for the home side, as it fought its way back from 16-8 down.
The Jaguares led 8-0 early, before a darting run from Brad Weber led to Chiefs flanker Lachlan Boshier touching down.
A penalty by first five-eighth Jack Debreczeni made it 10-8 at halftime, before the Chiefs scrum began giving it further ascendancy.
That allowed Debreczeni and Marty McKenzie to kick two more penalty goals and give the visitors an eight-point lead.
However, Moroni's try and two penalties allowed the Jaguares to score 13 points in eight minutes and edge ahead to claim victory.
In the last quarterfinal the Brumbies were far too good for the Sharks in Canberra.
They booked their ticket to Buenos Aires next week with a 38-13 win.
Pete Samu scored twice, while Henry Speight also crossed to give the Brumbies a 24-6 halftime lead.
Andre Esterhuizen got one back for the Sharks, but it was as close as they got.
Joe Powell and Matt Lucas both touched down in the final 10 minutes to give the Brumbies a convincing win.
On Friday night the Highlanders were beaten 38-14 by the Crusaders in Christchurch.
Jaguares 21 (Pablo Matera, Matias Moroni tries; Joaquin Diaz Bonilla con, 3 pen)
Chiefs 16 (Lachlan Boshier try; Jack Debreczeni con, 2 pen, Marty McKenzie pen).
Halftime: 10-8 Chiefs.
Hurricanes 35 (Salesi Rayasi 2, TJ Perenara, Ben Lam tries; Beauden Barrett 3 con, pen, Jordie Barrett 2 pen)
Bulls 28 (Cornal Hendricks 2, Warrick Gelant tries; penalty try; Handre Pollard 3 con).
Halftime: 24-14 Hurricanes.
Brumbies 38 (Pete Samu 2, Henry Speight, Joe Powell, Matt Lucas tries; Christian Lealiifano 5 con, pen)
Sharks 13 (Andre Esterhuizen try; Curwin Bosch con, 2 pen).
Halftime: 24-6 Brumbies
Jaguares (2) v Brumbies (3), Buenos Aires, Saturday, 11.05am
Crusaders (1) v Hurricanes (4), Christchurch, Saturday, 7.35pm