Wild-card Bouchard stands in the way of Konta and place in the Sydney final
At a set and a break up, the British No 1, seeded sixth here, appeared to be coasting towards a last four place but her Russian opponent broke back immediately and then again to establish a 4-2 lead.
Konta, who made 31 winners and 30 unforced errors, dug deep to win five of the next six games for a 6-3 7-5 victory in just under an hour and three-quarters as she set up a showdown with Canadian wild-card Eugenie Bouchard, who enjoyed a 6-2 6-3 victory over Anastasia Pavlyuchenkova.
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Hide AdKasatkina, ranked 16 places below Konta at 26 in the world, claimed an upset win over world No 1 Angelique Kerber on Tuesday but was left to rue making double the amount of unforced errors as winners – 30 to 15.
Barbora Strycova survived a marathon against Caroline Wozniacki in the heat to reach the semi-finals.
The pair battled for three hours and 20 minutes before the Czech claimed a 7-5 6-7 (6/8) 6-4 victory.
Strycova, the world No 19, next meets second seed Agnieszka Radwanska, who was a much more comfortable 6-3 6-2 winner over qualifier Duan Ying-Ying.
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Hide AdDan Evans mounted an impressive comeback to upset eighth seed Marcel Granollers and reach the quarter-finals of the men’s competition in Sydney.
The British No 3, ranked 67, struggled in the first set, but hit back impressively to win 1-6 6-3 6-3 in an hour and 43 minutes.
Evans was particularly dominant on his first serve, losing only seven points, and a single break in each of the last two sets was enough to topple the world No 37.
There was defeat for British No 8 Brydan Klein in the second round of the ASB Classic in Auckland, Joao Sousa proving too strong in a 6-3 6-4 triumph.