Ukraine's Elena Svetolina, the world number six on Wednesday, was booked to the Singapore Masters Championship, which brings together the world's eight best players next week as Czech Republic's Carolina Pleskova finished fifth in the second round of the Moscow International Tennis Tournament.
Tunisia's Anas Gaber blew off a surprise upset with a 3-0 win over Stevens in the second round with a 6-3, 6-2 win in 63 minutes.
Pleskova, second seed in Moscow and China's Tianjin champion on Sunday, lost to Russian Vera Zvonareva 1-6, 2-6 in 71 minutes.
Zvonareva will meet fifth seed Anastasia Sevastova of Latvia, who beat Kazakhstan's Yulia Potentsva 7-5, 4-6, 6-4.
Pleskova's chances of being in the final stand on the failure of Dutch Kiki Pattens, the world's tenth, and fourth in the Moscow tournament to reach the role of four according to the Association of Professional Athletes.
Bartens was eliminated from the first round of the first four titles, and will begin her career on Wednesday with Belarusian Alexandra Sasenovic 31 to reach the quarter-finals.
The number of women participating in the Masters Championships has risen to seven as well as Svetolina, who will be ranked seventh in the Masters Series, the Romanian Simona Halib first world, German Angelique Kerber, Danish Caroline Wozniacki, Japanese Naomi Osaka, Czech Petra Kvetova and American Sloan Stevens, Pleskova and Bertens.
Tunisia's Anas Gaber of the qualifiers meet eighth-seeded Anit Contavet of Estonia, who beat Frenchwoman Christina Mladenovic 6-2, 7-6 (7-3).
Gaber beat Russian Ekaterina Makarova 6-1, 6-2 in the first round.
