The loss came after a brilliant opening-round win against No. 10-ranked Petra Kvitova.
This is Samsonova’s first appearance at Wimbledon, and she is just one of two wild cards remaining in the women’s singles event.
“That’s pressure,” she said on court after the match when told no woman has ever won Wimbledon as a wild card.
Samsonova earned a double break to take the first set comfortably but struggled in the second.
However, she regained her confidence in the deciding set and broke Stephens in the opening game. Her service remained strong with four aces. She hit 31 winning points to Stephens’ four.
Elsewhere on Friday, No. 2-seeded Aryna Sabalenka is into the second week at Wimbledon and on the verge of a career breakthrough.
The hard-hitting Belarusian beat qualifier María Camila Osorio Serrano 6-0, 6-3 to reach the fourth round, and she might be overdue for a deep run in a Grand Slam. Sabalenka is the only woman among the top 20 seeds who has yet to reach a major quarterfinal.
The time seems right for that to change: Sabalenka leads the tour with 32 match wins this year, her seeding is a career high in a major, and she’s navigating a draw already without eight of the 11 highest-ranked women.
“I just keep working, keep improving,” Sabalenka said. “Every match is a new match. You never know what is going to happen.”
She overpowered Osorio Serrano, and pulled away when the Colombian went 0-for-6 converting break points in the first set.
“So many chances,” Osorio Serrano said. “I couldn’t close it.”
Also still in contention is No. 7-seeded Iga Świątek, the 2020 French Open champion, who breezed into the fourth round by beating Irina-Camelia Begu 6-1, 6-0. Świątek seeks a Wimbledon double after winning the girls’ singles title in 2018.
“It would be amazing,” she said. “It’s another Grand Slam, so it’s like a dream come true for any of us.”
No. 8 Karolina Pliskova swept Tereza Martincová 6-3, 6-3.
ESPN’s Kathleen McNamee contributed to this report.