Australia reached the knockout stage for the first time after losing in the group stage last year
Great Britain missed out on the United Cup quarter-finals as Australia qualified from Group C with a 2-1 victory over the United States.
Hosts Australia reached the last eight asStorm Hunter and Matt Ebden beat Jessica Pegula and Rajeev Ram in a mixed-doubles decider.
Earlier, Pegula beat Ajla Tomljanovic to level after Australia’s Alex de Minaur beat Taylor Fritz.
Australia’s win meant GB were edged out, finishing third in a tight group.
All three nations won one and lost one of their two ties in Perth, as well as each finishing tied on three match wins and three losses.
That meant the number of sets won was used to decide who progressed to the quarter-finals and Britain, who made a winning start against Australia before losing to the United States, missed out.
The Americans, who are the defending champions, must wait to see if they qualify as one of the best group runners-up.
The winners of six groups go into the last eight and will be joined by the best runner-ups in each of the host cities – Sydney and Perth.
Australia and Poland, who finished as Group A winners, are the first through in the 18-nation event which is a mixed-gender team format and offers $10m (£7.85m) in prize money.
Top seeds Poland, led by women’s world number one Iga Swiatek, secured their place in the quarter-finals on Monday with a 2-1 win over Spain.
Four-time major champion Swiatek won 6-2 6-1 against Sara Sorribes Tormo in Perth before partnering Hubert Hurkacz to thrash Sorribes Tormo and Alejandro Davidovich Fokina 6-0 6-0 in the mixed doubles decider.
In Group D, France won 2-1 against Germany as Caroline Garcia and Edouard Roger-Vasselin saved match points before beating Angelique Kerber and Alexander Zverev 7-6 (7-4) 2-6 12-10.
France could win the group if they beat Italy on Wednesday.
In Group B, Norway gave themselves hope of qualifying as two-time major finalist Casper Ruud earned a pair of wins in a 2-1 victory over Croatia in Sydney.