It took Stephens three sets to beat Bertens 7-6, 2-6, 6-3 at the Kallang Tennis Centre, preventing Osaka from exiting the competition after she lost 6-4, 5-7, 6-4 to Kerber.

"Whenever I want to win badly, then it starts becoming emotional, and I can't really control too much, like when it starts going a bit sideways," Osaka, the US champion, said.

"Usually when I win is when I can control it, so I'm just gonna try to do better on that part."

The end of season competition pits the world's eight best players against each other in a round robin tournament. 

The eight are split into two groups of four with the top two from each progressing further into the competition.

Stephens now has two wins to her name, while Kerber and Bertens have one each and Osaka has none.  

Osaka risked elimination after recording her second loss, but following Stephens' victory, any of the red group can still qualify.

The qualifiers will be decided on the last day of round robin play.

Tomorrow's action will see Karolína Plíšková of the Czech Republic against compatriot Petra Kvitová, while Dane Caroline Wozniacki meets Ukraine's Elina Svitolina. 

Both games are in the white group.