Cameron Norrie and Katie Swan gave Great Britain the perfect start to their United Cup campaign as their victories contributed to a 2-0 lead over Australia in Sydney.
Swan broke serve in her first three return games en route to a 6-4 6-3 win over world number 772 Zoe Hives.
Harriet Dart can win the tie if she beats Ajla Tomljanovic on Friday.
Dan Evans will then face Jason Kubler on Friday, ahead of a doubles match in which Evans and Dart take on Sam Stosur and John Peers.
The inaugural mixed-team tournament involves six round-robin groups of three teams.