Bertens' serve was on form to take the first set 6:3

However, in the second set, Kontaveit, 24, from Tallinn broke her opponent's serve twice, taking the scoreline in games to 5:1. She dropped one more game before winning the set 6:2.

In the deciding set, the Estonian did break her opponent's serve again, but failed to capitalize on it. The scoreline in games remained very even, ending up at 5:5 at one point. However, Bertens won the next game, and found herself with two matchpoints in the one after which, although Kontaveit staved off the first, was enough to ensure Bertens, who faces world number three Naomi Osaka (Japan) next, took the match.

Kontaveit won her first round game at the Queensland Tennis Center on Tuesday, defeating Su-wei Hsieh of Taiwan in straight sets, 6:4, 6:1.

Today's game was the second time this week the Estonian had lost to Bertens; the latter, together with her partner, world number one and local hero Ashleigh Barty, defeated Kontaveit and her partner Anastasia Pavlyuchenkova in three sets in the ladies doubles on Monday.

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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