Cincinnati - Ashleigh Barty held off Anett Kontaveit as the Estonian served for victory before the Cincinnati top seed scraped a 4-6, 7-5, 7-5 victory on Thursday to reach the quarter-finals.
The win keeps the Australian in the chase for a possible return to the WTA number one ranking which she lost to Naomi Osaka on the eve of this US Open build-up event.
Barty needs to reach the Sunday final in order to regain the ranking summit.
"The key for me was to fight and hang in there. I wanted to fight for as long as I could," said Barty, the reigning Roland Garros champion.
"I trusted myself and my movement. I just wanted the opportunity to play as many matches this week as possible."
Victory came a day after Barty defeated five-time Grand Slam winner Maria Sharapova in the second round.
After losing the opening set, Barty fought back in the second, exchanging breaks with Kontaveit and breaking the Estonian once more in the 12th game to square the match.
Kontaveit broke for 4-3 in the third set and served for the win in the ninth game.
But Barty summoned all her resources and broke the last two Kontaveit service games to grab the win.
She will play on Friday against Maria Sakkari of Greece, a 6-7 (4/7), 6-4, 6-4 winner over ninth seed Aryna Sabalenka.
In the men's draw, Richard Gasquet put out Diego Schwartzman 7-6 (8/6), 6-3 while Japanese qualifier Yoshihito Nishioka reached his second quarter-final of the season when he defeated Australia's Alex de Minaur 7-5, 6-4.
The 77th-ranked Nishioka, who shocked compatriot Kei Nishikori on Wednesday, will next face either France's Adrian Mannarino or Belgian 16th seed David Goffin for a place in the semi-finals.
Nishioka, 23, advanced in 82 minutes, never facing a break point while twice breaking the Australian's serve.
Results on Thursday in the WTA/ATP Cincinnati Masters (x-denotes seeding):
Daniil Medvedev (RUS x9) bt Jan-Lennard Struff (GER) 6-2, 6-1
Richard Gasquet (FRA) bt Diego Schwartzman (ARG) 7-6 (8/6), 6-3
Yoshihito Nishioka (JPN) bt Alex De Minaur (AUS) 7-5, 6-4
David Goffin (BEL x16) bt Adrian Mannarino (FRA) 7-6 (8/6), 6-2
Ashleigh Barty (AUS x1) bt Anett Kontaveit (EST) 4-6, 7-5, 7-5
Maria Sakkari (GRE) bt Aryna Sabalenka (BLR x9) 6-7 (4/7), 6-4, 6-4
Venus Williams (USA) bt Donna Vekic (CRO) 2-6, 6-3, 6-3