Johanna Konta of Great Britain celebrates a point during her Singles first round match against Gabriela Dabrowski of Canada on day two of the Toray Pan Pacific Open at Arena Tachikawa Tachihi on September 18, 2018 in Tachikawa, Tokyo, Japan.
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Konta, 27, has struggled for form all season, failing to get past the second round in any of the four Grand Slams, but she has looked good so far in Moscow.
Having seen off Daria Gavrilova in the previous round and stunned Elise Mertens in the first round she got off to a brilliant start against Sasnovich as she took the opening set 6-2.
However, Belarusian opponent hit back by the same scoreline to force a deciding set.
Neither player dropped a set in the decider which forced the match to a tie-break.
In the first point Konta lost her serve but immediately broke twice to take the lead.
She broke Sasnovich on two more occasions to seal the tie-breaker 7-2.
Konta will now face the winner of the all-Russian clash between Anastasia Pavlyuchenkova and Daria Kasatkina in the final four.