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.
Australia to World Group II playoff in Fed Cup
Juande Ramos Hints At Real Madrid Debut For Faubert
Australia to World Group II playoff in Fed Cup
Exclusive: Indonesia - Hosting World Cup Is Not Impossible
