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.
Sabalenka produced three double faults as she tried to serve out the match against Pegula at 5-4 in the second set, but recovered to hold for love at the next attempt and clinched victory when the winless American was unable to hold her serve.
The WTA Finals is taking place in Fort Worth, Texas, after the event was moved from usual host city Shenzhen, in China, for the second successive year.
In December last year, the women's governing body announced the immediate suspension of all tournaments in China amid concern for Chinese tennis player Peng Shuai.
Peng, 36, disappeared from public view for three weeks after accusing a top Chinese official of sexual assault.