Hsieh took an early 3:2 lead in the first set, only for the Estonian to pull back to 5:3. Hsieh took the next game, with Kontaveit wrapping things up 6:4.

In the second set, Kontaveit was more in control, taking three of the first four games. Hsieh did not win any further games and Kontaveit, 24, from Tallinn ranked 26th in the world, won 6:1 to take the match

The whole encounter lasted one hour and ten minutes, with Kontaveit serving up eight aces and two double faults to Hsieh's one ace and five double faults, ERR's sports portal reports.

While Hsieh only won two of 11 break points, Kontaveit took five out of six, though the Estonian only had a 29 percent success rate on her second serve.

Kontaveit faces the winner of Kiki Bertens and Dayana Yastremska (Ukraine, ranked 22nd in the world).

Kontaveit and Bertens, world number nine, from the Netherlands, had already met in the doubles. Bertens and her partner, world number one and local hero Ashleigh Barty defeated Kontaveit and her partner Anastasia Pavlyuchenkova in three sets.

The competition is going ahead despite the widespread bush fires in Australia, including some burning close to Brisbane. Australian players including world men's number two Nick Kyrgios have helped to raise money towards the relief efforts.

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