One more win will send Australia through to a semi-final date with Belgium or Italy in September.
Thompson closed out a career-best win over world No.15 Jack Sock to break the quarter-final in Brisbane wide open for the home side before in-form Kyrgios took care of fellow big server John Isner to leave Australia one rubber from victory.
And the American duo made sure the USA would live to fight another day when they outlasted the Australian pair 3-6, 6-3, 6-2, 2-6, 6-3.
In ominous form during last month's U.S. 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.
Jim Courier was impressed by Nick Kyrgios´ performances this weekend in Davis Cup.
Hewitt added: "I couldn't be prouder of my boys".
Earlier in Brisbane, Australia advanced to the semifinals after Nick Kyrgios beat late substitute Sam Querrey of the United States 7-6 (4), 6-3, 6-4 in the first reverse singles match, clinching the quarterfinal 3-1 with a match to spare.
The Americans named Sam Querrey and Steve Johnson for Saturday's doubles rubber against John Peers and Sam Groth.
"It's going to be two tough matches tomorrow but we'll be up for the challenge".
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Isner said Kyrgios was now a more mature player than in their 2015 and 2016 matches. He's always there. He's given me so much support, I can't say enough.
Any hope of an Italy comeback were snuffed out by Goffin though who was ruthless against Lorenzi as he took his record to 13 wins in 14 Davis Cup singles matches.
"I haven't been going back to the hotel hating the game or just trying to get through every day".
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.
Lacking his opponent's court speed, Isner swung for the fences and scrapped to within two points of forcing another set, but two fierce returns off the Australian's racquet stole the momentum and set up Kyrgios for his match-winning 20th ace.
The American number one looked the more unsafe in the third but Thompson held on to force a tiebreak, gaining a vital break before taking the set when Sock double-faulted.
HONOURS EVEN IN NEW ZEALAND-SOUTH KOREA DAVIS CUP TIE: There were mixed fortunes for South Korea's young guns as they finished the opening day of a Davis Cup Asia/Oceania Group I tie level at 1-1 against hosts New Zealand.
"I thought (the crowd) really embraced me this time".
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