Cincinnati - Second-ranked Simona Halep charged closer to taking the world number one ranking on Thursday, beating Latvian 15th seed Anastasija Sevastova 6-4, 6-3 to reach the WTA and ATP Cincinnati Masters quarter-finals.
Romania's Halep, a French Open runner-up for the second time in June, can overtake top-ranked Czech defending champion Karolina Pliskova by winning the title in the final major tuneup for the US Open.
"To be number one in the world I think is a big thing," Halep said this week. "If I deserve the place, for sure I will win it."
Pliskova, who faces Italian qualifier Camila Giorgi in a later third-round match, must also fight off Ukraine's Elina Svitolina, who won her fifth WTA title of the year last week in Toronto to reach a career-high fourth in the rankings. Svitolina faces Germany's Julia Goerges later.
"Of course to be number one is a goal of mine," Svitolina said. "The important thing is to play well at the big tournaments. Then the ranking will be there."
Spaniard Rafael Nadal, the 15-time Grand Slam champion assured of returning to world number one next week, faces countryman Albert Ramos-Vinolas in a night match. Nadal could meet Australian Nick Kyrgios in Friday's quarter-finals.
Nadal was assured advancing past injured Andy Murray for the top spot when Roger Federer withdrew from Cincinnati on Monday with a back injury.
After an early exchange of breaks, Halep double faulted to surrender another and give Sevastova a 3-2 edge.
She then had a visit from her Australian coach, Darren Cahill, who encouraged more backhands but closed with, "This is on you. Turn this around."
Halep did, breaking to 4-4 and again to claim the set when the Latvian swatted a backhand beyond the baseline.
Sevastova squandered two break points in the first game of the second set and netted a backhand to give Halep a 2-0 edge, but broke back in the fifth game.
Halep responded with a drop volley winner to break the Latvian at love for a 4-2 lead and held twice to capture the match after 78 minutes, improving to 5-3 lifetime against Sevastova.
"It was really difficult," Halep said. "She's a very tough opponent. I wasn't concentrating on anything else but winning the match."
Halep, who won her 15th career title earlier this year at Madrid, next faces either British seventh seed Johanna Konta or Slovakian 11th seed Dominika Cibulkova.
Also reaching the quarter-finals was eighth seed Svetlana Kuznetsova, who eliminated Spain's Carla Suarez Navarro 6-2, 6-4. The 32-year-old Russian, a two-time Grand Slam champion, next faces either American Madison Keys or Wimbledon champion Garbine Muguruza of Spain.