Cameron Norrie beat Taylor Fritz in three sets but Great Britain trail their United Cup play-off against the United States 2-1.
British number one Norrie won 6-4 5-7 6-4 in the Sydney City Final, after team-mate Katie Swan had earlier lost 2-6 6-3 6-4 to American Madison Keys.
Harriet Dart was then beaten 6-2 6-0 by world number three Jessica Pegula.
Dan Evans faces Frances Tiafoe in the final singles rubber in a bid to keep alive GB's hopes of progression.
Should he win, he and Dart will then take on Tiafoe and Pegula in the deciding doubles.