Kontaveit, who recently fell one place in the WTA rankings, to 30th, saw her opponent take control in the opening set, winning two games before the Estonian was able to bag her sole game of the set.

However, while Davis, ranked 97th in the world, wrapped up that set convincingly, the following two saw the tables turned, as she failed to win a single game more.

The entire encounter lasted one hour and 35 minutes, while both players served up four aces and committed three double faults each.

The result also ends a recent streak which saw Kontaveit go out in round one in her last three competitive matches - starting with the olympics and followed by tournaments in Montreal and in Cincinnati.

Kontaveit meets Caroline Garcia (France), ranked 61st in the world, in round two. Garcia defeated another local player, Catherine Harrison, in straight sets in her round one match.

The pair have met in competition four times before, with the victory tally even at two each.

The tournament is hosted at the Jacobs Pavilion in Cleveland, OH, and is played on outdoor, hard courts, as will be the U.S. Open.

Kontaveit has a new coach, former player Dmitry Tursunov, who she hired earlier this month, on a trial basis.

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