Australia have won promotion to the Fed Cup World Group after US Open winner Samantha Stosur gave her team an unassailable 3-0 lead over Germany on Sunday in their play-off tie.
Stosur, ranked fifth in the world, needed only 74 minutes to see off Germany's Andrea Petkovic, ranked 11th, for a 6-4, 6-1 victory in the third singles rubber which settled the promotion/relegation tie.
It was the first time Petkovic had played since January having taken time off to heal a persistent back injury.
The defeat means Germany will drop to World Group II, while Australia will join the eight-team elite top-tier.
It was Stosur's second victory of the weekend after she also saw off Germany's Angelique Kerber 7-6 (7/1), 6-4 in a tie-breaker in Saturday's opening rubber.
Team-mate Gajdosova, 50th in the world, then blasted Julia Goerges, ranked 16, 6-4, 6-4 to give the guests a 2-0 lead going into Sunday.
Although the tie is now decided, the final two rubbers are still to be played on Sunday with Kerber up against Fed Cup-debutant Olivia Rogowska in the singles.
Stosur will then team up with Casey Dellacqua to take on Anna-Lena Groenefeld and Goerges in the doubles.