The combustible Kyrgios came back from two sets to one down to defeat 33-year-old Steve Darcis 6-3, 3-6, 6-7 (5/7), 6-1, 6-2 in 3hr 36min on the clay courts of Brussels' Palais 12 arena.
Kyrgios fired 34 aces and 41 winners to take his Davis Cup singles record to seven wins in eight, as Australia finished the day at 1-1 after world number 12 David Goffin had beaten 185-ranked John Millman 6-7 (4/7), 6-4, 6-3, 7-5.
Kyrgios, defeated in the first round of the US Open by compatriot Millman earlier this month, went into the match suffering a hip injury as well as a lack of motivation.
Writing on www.playersvoice.com, the 22-year-old said: "I am not [what] professional tennis needs me to be. I'm not making the improvements I should because I don't want it enough, I'm not taking it seriously enough. There is a constant tug-of-war between the competitor within me wanting to win, win, win and the human in me wanting to live a normal life with my family away from the public glare."
However, he was overjoyed by his performance in Brussels as Australia, the 28-time champions, seek a place in the Davis Cup final for the first time since they last won the title in 2003.
"(Captain) Lleyton Hewitt and I have put so much dedication into this, the Davis Cup has been my No.1 priority this year. I think we must be favourites going into the doubles' tomorrow," Kyrgios told daviscup.com.
Jordan Thompson and John Peers will play the doubles against Arthur De Greef and Ruben Bemelmans with the reverse singles to be played on Sunday.
In Lille, Dusan Lajovic made a mockery of the absence of Novak Djokovic to give Serbia a shock lead over France in their semi-final.
World number 80 Lajovic edged Lucas Pouille, ranked 58 places higher, 6-1, 3-6, 7-6 (9/7), 7-6 (7/5) in the first rubber of the tie also being played on clay.
"This is what the Davis Cup is all about," said Serbia captain Nenad Zimonjic, who is without his three leading singles players — Djokovic, who is sidelined until 2018 with a wrist injury, Janko Tipsarevic and Viktor Troicki.
However, France, the nine-time champions, levelled the tie at 1-1 when Jo-Wilfried Tsonga downed Davis Cup debutant and world number 95 Laslo Djere, 7-6 (7/2), 6-3, 6-3.
France captain Yannick Noah was critical of his own performance.
"I did not have a very good match as a captain. I was a bit stressed and I think I passed my stress to Lucas," he said. "I'll have to improve our communication for the next rubber."
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