The trio of Melissa Hoskins, Amy Cure and Ashlee Ankudinoff posted the fastest time in the qualifying round to book themselves a spot in the final against hosts Great Britain.
Australia led for much of the 3km final, with Great Britain coming from behind to take the win in a close match, much to the delight of their home crowd.
The Great Britain team, which consisted of junior world champion Elinor Baker and Olympic Champions Laura Trott and Dani King, stopped the clock at 3min 21.043sec to claim gold. The Australians team completed the distance in 3min 22sec.
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Earlier Belarus beat Lithuania for the bronze medal.
Australia did not field a men's team pursuit, with omnium world champion Glenn O'Shea the only male endurance rider competing at this round of the world cup.
O'Shea got off to a strong start in the omnium, finishing third in the flying lap in a time of 13.354.
A rough points race which was dominated by Ukraine's Volodymyr Kogut and Spaniard Unai Elorriaga saw O'Shea finish in twelfth position.
O'Shea recovered from his disappointing points ride to finish second in the elimination race behind Elorriaga.
There was a European flavour to the men's team pursuit with Denmark catching the Germans in the final after they fell apart due to a fast start. Belgium collected the bronze medal.
The event got off to a bad start for the hosts with Great Britain's men's team pursuit crashing heavily in the qualifying round.
The team, who did not include any of the Olympic champions, touched wheels with four laps remaining.
Sam Harrison, Joe Kelly and world champion Andrew Tennant all come off their bikes with the rider in first position, Owain Doull, the only one to stay upright.
