Dokic, who reached the quarterfinals at the Australian Open last week in her first Grand Slam appearance in three years, beat Thailand's Suchanan Vitraprasert 6-1, 6-2 to give Australia a 1-0 lead.
Samantha Stosur was down a set and trailed 2-5 before she broke Tamarine Tanasugarn's serve to spark an 11-game roll for a 4-6, 7-5, 6-0 win that gave Australia a winning 2-0 lead.
Casey Dellacqua and Rennae Stubbs combined to beat Noppawan Lertcheewakarn and Varatchaya Wongteanchai 6-4, 6-2. The Australians beat South Korea 3-0 to start the tournament and would have to lose every match against Taiwan on Friday to miss the final.
In the other Group B match, South Korea won both singles matches before Taiwan rallied to win the doubles.
In Group A, Indonesia had a 3-0 win over an India team missing star player Sania Mirza, who withdrew from the tournament with torn abdominal muscles.
New Zealand beat Uzbekistan 2-1 to remain unbeaten.
The top teams in each group will play a final to decide which country advances to the World Group II playoffs in April.
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