Belinda Bencic won a tricky encounter against Anna Karolina Schmiedlova while Madison Keys hammered Daria Kasatkina.
It was a day of mixed emotions for the stars of the women's tour on Tuesday.
Barty advanced to the semi-finals of the WTA Finals with a straight-sets win over Kvitova, while Bencic progressed when Bertens retired.
Belinda Bencic withstood a second-set fightback from Petra Kvitova to earn a vital win that keeps her in the running at the 2019 WTA Finals.
Ash Barty finishes day one at the top of the Red Group at the WTA Finals after a three set win over Belinda Bencic.
Belinda Bencic is delighted after not only reaching the Moscow Final and qualifying for the WTA Finals.
Belinda Bencic is one win away from qualifying for the WTA Finals after beating Kirsten Flipkens in the Moscow Quarter-Finals.
Belinda Bencic praised her fighting qualities as she reached the Moscow Quarter-Finals.
Belinda Bencic beat her good friend Donna Vekic in straight sets to advance to her first-ever Grand Slam semi-final at US Open 2019.
Belinda Bencic powered past an under-par Naomi Osaka in straight sets to reach the US Open Quarter-Finals.
Karolina Pliskova made an impressive start to French Open 2019 with a comfortable straight-sets win over Madison Brengle.
Karolina Pliskova cruised to a straight-sets victory over Tomljanovic in Rome, while Bencic produced a stunning comeback to beat Sevastova.
The Romanian is closing in on another title at her 'special tournament.'
Belinda Bencic is into the Madrid semi-finals after a three set win over world number one Naomi Osaka.
Naomi Osaka maintained her grip on the World No.1 ranking with a serene straight-sets victory over Su-Wei Hsieh in Stuttgart.
Anett Kontaveit started her clay court campaign in style with a straight-sets win over Caroline Garcia at the Porsche Tennis Grand Prix.
2018 Champion Kiki Bertens crashed out of the Volvo Car Open in the third round with a straight-sets loss to Maria Sakkari.
The former world No.1 is a win away from playing in her first final for eight months.
Belinda Bencic marched on into the semi-final of the BNP Paribas Open with a hard-fought three-set win over Karolina Pliskova.
Belinda Bencic came up with some breathtaking tennis to knock out defending champion Naomi Osaka in Indian Wells.