Russian Kuznetsova needs to defend her title in Moscow this weekend to claim the eighth and final spot in the season-ending tournament in Singapore next week.
Sixth-seeded Sock downed German fourth seed Alexander Zverev 6-7 (4/7), 7-6 (7/4), 6-4 in the other semi-final.
Konjuh, ranked 58, endured service woes as she double-faulted seven times and was broken on five occasions to bow out.
In the other semi-final, Julia Goerges of Germany, who saw off eighth-seeded Daria Kasatkina of Russian Federation 7-5, 6-1, will clash with Australia's Daria Gavrilova, who beat Anastasia Pavlyuchenkova, seeded seventh, 7-5, 4-6, 6-3.
BBC tennis correspondent Russell Fuller said she has arrived in Singapore, and appears fit to play.
"It has been a great week and I am playing with no pressure so I will go out on Saturday and play my game and see what happens".
Kuznetsova is already assured of her best year-end ranking since 2009 and is aiming to defend her Moscow title in front of a home crowd. Konta entered the world top-10 following her performance at the China Open.
Disappointed Daria Gavrilova
Kuznetsova played a full Asian swing and also several European events in order to make it to WTA Finals: "I felt exhausted in the morning practice, didn't know how I would have played".
Germany's Julia Goerges or Daria Gavrilova of Australia await in the final, with Konta no doubt hopeful one of those will do her a huge favour.
Daria Gavrilova earns the first ever WTA final appearance of her career in the city where she was born twenty-two years ago.
World number one Angelique Kerber is in the Red Group alongside Simona Halep, Madison Keys and Dominika Cibulkova.
She only took 53 minutes to secure a 6-2 6-0 win where she reeled off the last 11 games after going 2-1 down in the opening set.
Kuznetsova is scheduled to face Agnieszka Radwanska in round robin play on Monday.