Storm Sanders (28) dispatched Alison van Uytvanck (28) 6-2 6-2 and Ajla Tomljanovic (29) rallied from a set and a breakdown before Elise Mertens (26) retired injured while trailing 4-6 6-4 3-0 to earn Australia their second Group B win after they saw off Slovakia in the opening tie.
Sanders returned to court and teamed up with Sam Stosur (38), seeing off Ysaline Bonaventure (28) and Kirsten Flipkens (36) 6-4 6-3 to complete the clean sweep.
Britain also booked a semi-final spot from Group C after Alicia Barnett (29) and Olivia Nicholls (28) sealed a surprise 3-0 win over Spain and they face Australia on Saturday.
Barnett and Nicholls beat Spain's Aliona Bolsova (25) and Rebeka Makarova (23) 7-6(5) 6-2. Heather Watson (30) defeated Nuria Parrizas Diaz (31) 6-0 6-2 and Harriet Dart (26) earned a surprise victory over Paula Badosa (24) 6-3 6-4.
Canada won by a 3-0 score against Italy after Bianca Andreescu (22) and Leylah Fernandez (20) claimed impressive singles victories to help them get their campaign off to a perfect start.
Andreescu overturned a 5-2 deficit in the first set and battled back from 2-0 down in the second to beat Elisabetta Cocciaretto (21) 7-6(3) 6-3, while Fernandez thrashed Martina Trevisan (29) 6-0 6-0 in only 44 minutes.
Fernandez carried that ruthless streak into the doubles, joining forces with Gabriela Dabrowski (30) to beat Lucia Bronzetti (23) and Jasmine Paolini 6-1 6-1.
Canada will take on Switzerland, who swept Italy 3-0 on Wednesday, in their final Group A tie on Friday, with the winner advancing to the semi-finals.
Spain will play Britain in Group C while the Czech Republic will take on Poland in Group D later on Thursday.
