Belarusian seventh seed Aryna Sabalenka improved her chances of reaching the WTA Finals last four with a 6-3 7-5 win over American Jessica Pegula.
Sabalenka, 24, can only be stopped from qualifying by Tunisia’s Ons Jabeur winning in straight sets against Greece’s Maria Sakkari later on Friday.
Any other result – a Sakkari victory or Jabeur winning in three sets – sees Sabalenka through for the first time.
Fifth seed Sakkari, 27, is already assured of progressing as group winner.
The season-ending event sees the world’s eight best players this season split into two groups of four.
After the round-robin matches, the top two in each group move through to Sunday’s semi-finals.
French sixth seed Caroline Garcia and Russian eighth seed Daria Kasatkina meet on Saturday, with the winner finishing runner-up in the other group and playing Sakkari in the last four.
Poland’s world number one Iga Swiatek has already won that group and faces Sabalenka or Jabeur.