Dokic, who advanced to the quarterfinals at the Australian Open last week, beat Diane Hollands of New Zealand 6-4, 6-4. Dokic trailed 3-0 in the first set and 2-0 in the second.
Stosur then clinched the Asia/Oceania Zone I playoff promotion match for Australia with a 6-1, 6-4 win over New Zealand No. 1 Marina Erakovic. Stosur is ranked No. 43 and Erakovic 57th.
Australia's Casey Dellacqua and Rennae Stubbs beat Kairangi Vano and Shona Lee 6-2, 6-2 in doubles to give Australia its fourth straight 3-0 win at the tournament.
"I am happy with the way I have handled matches mentally this week,'' Dokic said. "I didn't play well (today) but you have to win even if you don't play well. I won the key points so I am happy with that.''
Dokic has a 12-2 singles record playing Fed Cup for Australia and won all three of her matches in Perth this week.
Australia has beaten New Zealand five times in a row in Fed Cup play since 1965.
The Australians reached the Group I final by dropping only one set in leading Pool B. New Zealand beat Indonesia 2-1 on Friday to top Pool A.
India was relegated to Group II after it was beaten 3-0 by Taiwan on Saturday.
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