The Australia Green pairing had been on the cusp of being eliminated from the tournament yesterday when they faced a match point against France’s Kenny De Schepper and Caroline Garcia, as a loss would have put the British team through.

Having come back to win that tie to become the first Australians since Lleyton Hewitt and Alicia Molik in 2003 to reach the final, the duo were understandably buoyed ahead of the clash against Ukraine's Elina Svitolina and Alexandr Dolgopolov.

Gavrilova, the 21-year-old Summer Youth Olympic gold medallist and US Open girls champion in 2010, rose to the challenge of playing an opponent ranked 17 places higher than her in the world rankings by claiming the first set 6-4 against Svitolina.

The Russian-born player, though, was made to work hard for her victory as the second set went to a tie-break.

Svitolina opened up a 6-1 advantage to look on course to level the tie, but Gavrilova hit back with seven straight points to win the match 6-4, 7-6 and put Australia Green into a 1-0 lead.

“I played a tournament in under-12s, and it was a super tiebreaker,” Gavrilova said after her win.

"I was down 9-1 and I ended up winning.

“I just literally told myself to settle down, just stop thinking of everything, just think about how to win every point.

“I just played free.”

Gavrilova’s victory put Australia on the brink of their second Hopman Cup title, with their only success to date in their home competiton coming in 1999, when Mark Philippoussis and Jelena Dokic overcame Sweden’s pair Jonas Bjorkman and Asa Carlsson.

The controversial Kyrgios, who was given a suspended 28-day ban for comments he made about Stanislas Wawrinka’s girlfriend during a Rogers Cup match in August, made a bright start in his first ever clash with Dolgopolov.

Having claimed the opening set 6-3, the 20-year-old continued his impressive display by securing the second 6-4 to seal victory for the home team.

With Australia Green having already won the tie, the mixed doubles match did not take place.

The straight sets win also maintained Kyrgios’ unbeaten record at this year’s tournament, with four singles and three mixed doubles victories, as he builds towards the Australian Open which begins on January 18.