The third-seeded Sakkari, who was leading 6-2, 1-0 when Kalinskaya retired, became the first Greek woman to qualify for the season-ending event for the top eight players. 

''It's achieving one of my biggest goals this year, it's very satisfying," Sakkari said. 

Former champion Simona Halep also advanced by beating home favorite Veronika Kudermetova 6-1, 7-6 (4) and Anett Kontaveit ousted Andrea Petkovic 6-1, 6-4. 

In the men's tournament, Adrian Mannarino saved a match point before beating defending champion Andrey Rublev of Russia 5-7, 7-6 (4), 6-3 to reach the quarterfinals. 

Mannarino faced the match point when trailing 6-5 in the second set but saved it when Rublev netted a backhand. 

It was a rematch of 2019 final, which Rublev won. 

''Two years later, it is completely different," Mannarino said. ''We have both improved. Andrey has improved a lot more than I. Even if a player is better than you, anything can happen. I got a little bit lucky today and I am really happy with my performance.'' Second-seeded Aslan Karatsev advanced by beating Egor Gerasimov 6-4, 6-3 to set up a quarterfinal against Gilles Simon, who beat American Mackenzie McDonald 6-3, 6-2.