Top seed Elina Svitolina was forced to dig deep before overcoming Chinese outsider Wang Qiang in her opening match at the Dubai Tennis Championships.
The defending champion had a bye into the second round, but needed more effort than she might have expected to get past her 46th-ranked lucky-loser opponent, before winning 6-1 5-7 6-2
"I didn't expect it like this," Ukrainian Svitolina said. "But I always try to expect the unexpected.
"I was a little bit angry at myself that I didn't bring my best game in the end of the second set but I had to accept it and bounce back."
Svitolina next plays for the semis against Japan's Naomi Osaka, who beat Anett Kontaveit 6-2 7-6 (7-5).
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German Angelique Kerber earned her second straight-sets win in 24 hours, 6-4 6-2 over Italian Sara Errani.
Kerber, the Sydney champion and Australian Open semi-finalist, will next face another former world No.1 in Karolina Pliskova, a winner over Spain's Carla Suarez Navarro 5-7 6-2 6-4.
"It was a tricky match, especially because she was playing well," said Kerber, who needed 64 minutes and five breaks of serve to take victory.
"I was just trying to stay in the match and not thinking about how she was playing."
Russian Elena Vesnina out-lasted French Open winner Jelena Ostapenko, the Latvian fourth seed, 6-1 7-6 (8-6).
Johanna Konta was unable to take either of two match points as she lost a marathon encounter to Russia's Daria Kasatkina.
The British No.1 led by a set and 3-1 and looked on the brink of victory at 6-4 in the second-set tie-break, but Kasatkina won four straight points, taking the set with a winner that just clipped the baseline.
The 20-year-old then proved the more consistent in the decider, wrapping up a 4-6 7-6 (8-6) 6-2 victory after two hours and 59 minutes to set up a quarter-final against countrywoman Vesnina.
