The Kazakh world number two blew a one-set lead in dramatic fashion at Roland Garros, slumping to a 3-6, 6-1, 7-6(4) loss.
"Honestly, hard to describe, I'm super happy," said world number 55 Starodubtseva after beating a top-10 opponent for the first time in her career.
"I'm super proud of myself that I was able to do this today. It was a tricky third set but I got it done in the end."
It is Rybakina's earliest exit from any WTA tournament since the 2025 Miami Open and first defeat in the opening two rounds of a major since the 2024 Australian Open.
Starodubtseva will face either in-form American 26th seed Hailey Baptiste or China's Wang Xiyu for a place in the last 16.
She has already matched her previous best run at a Grand Slam event, when she lost to Jasmine Paolini in the French Open third round as a lucky loser 12 months ago.