Both players had chances in a tight decider before Konta prevailed 6-2 2-6 7-6 (7-2) against the world number 31.

The victory takes Konta, who has dropped to 44th in the world rankings, into her first semi-final since June.

She will play Russian sixth seed Daria Kasatkina in the last four.

Konta, 27, split with her coach Michael Joyce last week and is working with Dimitri Zavialoff, a former coach of Stan Wawrinka, on a trial basis in Moscow.

She earned an impressive win over world number 16 Elise Mertens in the opening round and followed that by beating Daria Gavrilova in round two.

Against Sasnovich she raced into a one-set lead by winning four consecutive games from 2-2 but lost her opening service game of the second set with the Belarusian clinching it on her ninth break point of the game.

Sasnovich then comfortably levelled at one set apiece before both players failed to take break points early in the deciding set.

In the tie-break, Konta hit a fine backhand winner to move 4-2 in front and won the following three points to seal victory.