Aryna Sabalenka and Daria Kasatkina booked their places on Thursday evening, leaving one spot still to be decided.
Greek Sakkari and Russia's Kudermetova both beat other candidates for the season-ending tournament in Fort Worth, Texas, with Sakkari coming from a set down to see off Danielle Collins 5-7 6-3 6-3 and Kudermetova defeating Jelena Ostapenko 6-4 6-4 at the Guadalajara Open.
Now they will clash in the last eight on Friday, with Sakkari, who made her WTA Finals debut last year, saying on wtatennis.com: "It was meant to be. We both had very tough draws. It was not guaranteed that we were going to play each other in the quarter-finals.
"I think the passion, how much we want it, it got us to the point that we have to play each other just to get that one spot. It's going to come down to not who wants it more, but who plays a better match."
Kasatkina was beaten 6-2 2-6 6-3 by compatriot Anna Kalinskaya but will make her WTA Finals debut after other results went her way.
Madison Keys' hopes ended with a 6-4 6-7 (4) 6-1 defeat by Victoria Azarenka, who will take on Coco Gauff in the quarter-finals, while there will be an all-American clash between Sloane Stephens and Jessica Pegula.