U.S. captain Jim Courier threw another curve ball by sending world No.25 Querrey onto Pat Rafter Arena instead of No.15 Jack Sock, who was originally slated to face Kyrgios.
The Australian clinched the match in the fourth set by breaking Sock's service twice.
Kyrgios has been widely criticised in Australia for his on-court antics but he has responded well to Lleyton Hewitt's captaincy and was in sublime form as he downed John Isner on Friday to give Australia a 2-0 lead.
In ominous form during last month's United States hard-court swing, Kyrgios blasted 20 aces to Isner's 15, largely defusing the towering American's serve to close out a slow-burning singles rubber in 2 hours, 24 minutes. The British player, drafted into the singles line-up after the injury-enforced withdrawal of world number one Andy Murray, was made to pay for letting slip a 5/2 lead in the second-set tiebreak. "Ever since Melbourne, we all kept the group chat going, we all kept supporting each other when we're on the road and then we always had one eye on it - or at least I did", Kyrgios said.
"It was good to come back here and have that support, I thought they really embraced me this time".
Australia will head into Saturday's doubles matchup with high hopes that they can take out the quarterfinal series, after being knocked out of the tournament past year by the United States.
Nick Kyrgios has sent Australia through to the Davis Cup semifinals, with an emphatic straight-sets win over American Sam Querrey.
Australia, captained by Lleyton Hewitt, will play Belgium in the semi-finals after they beat Italy 3-2 on Sunday. Every day, you get close to the tie, practice becomes a bit more intense.
Rep.Pelosi on internet privacy: "you should be very very scared".
However, the vote was closer this time with 15 Republicans siding with Democrats in the effort to retain the rule. Republicans and industry groups have blasted that discrepancy, saying it was unfair and confusing for consumers.
"We're still alive", said Courier.
They edged out Australians John Peers, ranked third in the world in doubles, and Sam Groth 3-6, 6-3, 6-2, 2-6, 6-3.
But the United States soon clicked, firing back to win the second and third sets as Sock rediscovered his touch and his confidence. "My game is feeling good", Sock said.
But teammate Jordan Thompson's 6-3, 3-6, 7-6 (7-4), 6-4 win over American Jack Sock, the highest-ranked player in the tie at No.15, set the Americans back on their heels.
Australia last won the Davis Cup in 2003.
Hewitt added: "I couldn't be prouder of my boys".
India sealed a 4-1 win against Uzbekistan in the second round of the Davis Cup Asia/Oceania Group I tie in Bangalore yesterday to advance to the World Group playoff.