The clash between world number 16 Kyrgios and the 23rd ranked Isner will follow Jack Sock's first meeting with 22-year-old Australian Jordan Thompson on the hardcourt of the Pat Rafter Arena.
Nick Kyrgios was up against fellow big server John Isner in the day's second match-up and the controversial Australian claimed only his second Davis Cup rubber win in straight sets 7-5 7-6 (7/5) 7-5 to give the hosts a surprise 2-0 lead. "I think everyone could see that he stopped looking for his forehand", Thompson said.
Australia' s Nick Kyrgios played John Isner in the second match of the series, and dominated, winning in straight sets over the American, now ranked 23 in the world.
The victor of the quarterfinal will play Italy or Belgium in September.
The fiery Kyrgios, often treated as the villain at overseas tournaments since he was suspended for not trying his best in a match last October, said he appreciated the support from the home crowd of 5780.
Isner battled to the end, saving a match point at 6-5 to take the third set into a tiebreak, then charging into a 5-2 lead.
Thompson won both singles in his Davis Cup debut against the Czech Republic in February, and the 79th-ranked Australian continued that form over No. 15 Sock, the highest-ranked player in the tie.
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The American No.2, who owns a Davis Cup win over Roger Federer, clouted the most aces on the ATP Tour a year ago, 1159, at an average of 23 per match, the majority of which were best-of-three-set encounters.
"But I have been playing great tennis and putting my head down and I returned really well today, so I am more than happy to get the win".
Australia's Sam Groth and John Peers are not low-ranked journeymen, as was the Swiss team Adrien Bossel and Henri Laaksonen.
US Davis Cup captain Jim Courier added: "I'm super proud of these guys today but it still will take a monstrous effort from us on day three".
Kyrgios, the in-form world number 16, stands in the way of the United States of America team, all of whom are ranked in the top 30 in singles.
The Americans can change on Sunday morning their nominated singles players and Sam Querrey has a last-start win to his credit over Kyrgios, last month in Mexico. "I'm used to five-set matches".
Thompson's first serve velocity averaged out at 190kmh through the first three sets, with his fastest ball clocking 222kmh, and he moved eagerly at the back of the court.