Kontaveit, ranked 27th in the world, was at one point 4-1 up in the first set against Brady, ranked 86th. She broke the American's serve in the eigth game to clinch the set.

In the second set Ms. Kontaveit lost the first three games, before pulling things back to 4-4. With the score in games continuing to remain even stevens, the set went to a tie break which Kontaveit won 7-4.

Ms. Kontaveit served five aces through the course of the match and made three double faults, compared with her opponents two aces and four double faults.

Her next opponent in the third round is Alison van Uytvanck of Belgium, ranked 47th.

Van Uytvanck, 24, grabbed an upset victory over the number three in the world, Garbiñe Muguruzat of Spain.

Playing in her fifth Wimbledon finals, Annett Kontaveit, 22, has not progressed beyond the third round to date. Her best performance so far in the singles came last year when she lost to Caroline Wozniacki, after winning the first set. Nonetheless she exacted revenge of a sort by defeating Wozniacki, of Denmark, the current world number two, in straight sets on the clay courts of the WTA Rome Masters in May.

Ms. van Utyvanck is playing in the third round for the first ever time.

The game between Kontaveit and Uytvanck is scheduled for tomorrow, Saturday.

Meanwhile former top Estonia ladies' player Kaia Kanepi has got through to the second round of the ladies' doubles, with her partner Andrea Petkovic of Germany.