Rybakina, the World No 1, announced on the eve of the tournament that she would not be able to defend her title in Indian Wells.
“I am really sad to inform all my fans and supporters that I unfortunately have to withdraw from the WTA Finals this year,” Rybakina said.
“I’ve had an incredible season but my body is just not physically ready to compete.
“I’m going to spend some time resting and recovering at home and getting myself ready for the 2027 season.”
Rybakina’s withdrawal saw Ukraine’s Marta Kostyuk called up as an alternate, but she was unable to make a winning start after suffering a 6-2, 6-4 defeat to Noskova.
The Wimbledon champion, making her WTA Finals debut, needed just 86 minutes to overcome Kostyuk, breaking down her opponent’s resistance with an aggressive baseline game and 20 winners.
Kostyuk, who was informed only a day earlier that she would be competing, struggled to find her rhythm as Noskova secured her third consecutive victory over the Ukrainian.
Gauff then produced an impressive performance to defeat fellow American Jessica Pegula 6-4, 6-7(7), 6-2 in a contest lasting two hours and 39 minutes.
The world No 3 took the opening set before Pegula fought back to force a decider, saving multiple set points in the second set after trailing 1-5.
However, Gauff regained control in the third, racing to a 6-2 victory and sealing the match on her third match point.
The results leave Noskova and Gauff with one win apiece in Group 1, while Pegula and Kostyuk will be looking to bounce back in their next matches.
