Daria Gavrilova had earlier defeated Elina Svitolina 6-4 7-6 (8-6) in the women's rubber of the mixed event.
Svitolina had six set points at 6-1 in the second-set tie-break but lost the last seven points of the match.
Kyrgios, ranked 30th in the world, beat Britain's world number two Andy Murray in the group stage on Wednesday.
The tournament hosts, who had two squads competing in the eight-team event, last won the competition in 1999.

Julie-Anne Wood started her career in her hometown of Milford Haven in 1999.
She has now become the Maritime and Coastguard Agency's head of maritime operations and oversees the co-ordination of search and rescue around the UK coast.
Up until now the role has always been held by a man.
Ms Wood, who started out as a part-time coastguard watch assistant, said what once had been a male-dominated industry had changed.
"[It's] very different these days. The Maritime and Coastguard Agency has incorporated women in everything they do," she said.
"In my experience, there have been no restrictions."
Of her new position, she added: "'It's a huge responsibility and a position that I'm very honoured to hold."
Before she became a coastguard, Ms Wood ran her own business providing safety training to fishermen and merchant seamen in Wales.
When an opportunity to become a coastguard watch assistant came up, she took the job and said she "never looked back".
Over the next nine years she climbed the ranks and now has one of the most senior roles in HM Coastguard, heading up the National Maritime Operations Centre in Fareham, Hampshire, and the 10 Coastguard Operations Centres around the UK.

The rules of the Orange Order prohibit members from attending Catholic Masses.
Mr Elliott and the former UUP deputy leader Danny Kennedy publicly attended the funeral of Constable Kerr in Beragh on Wednesday.
Both are members of the order. Mr Elliott is a former county grandmaster of Fermanagh.
When asked about their attendance an order spokesman told the BBC: "It is important that the Kerr family know they have widespread support throughout the community and the Orange Order offers sincere sympathy to them on the loss of their brave son."
A former Ulster Unionist leader and Orangeman David Trimble attended a funeral Mass in Donegal for some of the victims of the Omagh bomb in 1998 without any action being taken.
Away from public gaze, it is known that members do attend the funerals of Catholic friends without censure.
It appears the leadership intends the same thing to happen on this occasion as well.

Matthew Tvrdon, 31, of no fixed abode, admitted manslaughter on grounds of diminished responsibility. He also admitted seven attempted murder charges and one of dangerous driving.
Prosecutors will consult the victims' families over the next seven days.
At the moment Mr Tvrdon is still due to be tried next month.
Mr Tvrdon faces a total of 32 charges including counts of actual bodily harm with intent and grievous bodily harm with intent.
During the Cardiff Crown Court hearing, he also pleaded not guilty to murder and six counts of attempted murder.
His barrister told the court his client was suffering from paranoid schizophrenia.
Ms Menzies, 31, died on 19 October 2012 after Tvrdon ran her over at a fire station forecourt in Ely.
Others were injured in the incident which happened during the afternoon school run.
She was walking with two of her children when she was killed.
Nick Kyrgios secured the Hopman Cup for Australia Green by beating Alexandr Dolgopolov 6-3 6-4 to give his team a 2-0 victory over Ukraine in Perth.
[NEXT_CONCEPT]
A coastguard from Pembrokeshire has made history by becoming the highest-ranking woman in Her Majesty's Coastguard.
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The Orange Order will take no action against UUP leader and Orangeman Tom Elliott for going to Ronan Kerr's funeral Mass, the BBC understands.
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A van driver has admitted killing mother-of-three Karina Menzies in a series of hit-and-run incidents around Cardiff in October.