Great Britain's Harriet Dart defeated Maddison Inglis in straight sets to seal the team's tie win over Australia at the United Cup.
Inglis was a late call-up for the match after Ajla Tomljanovic withdrew with a knee injury.
Dart's 6-4, 6-4 win on Friday meant Britain were victorious with two matches to spare.
Dan Evans lost to Jason Kubler 6-3 7-6 (7-3) and Evans and Dart will compete in a doubles match later on Friday.
Great Britain will now prepare to face their other group opponents Spain, with the first match being contested between Norrie and Rafael Nadal on Saturday.