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. Samsonova's service remained strong with four aces. She hit 31 winning points to Stephens' four.
"It was obviously a tough match," Stephens said. "I thought that she played well. She has a good game to suit grass. It was tough, but I have to give her credit. She played a good match. Sometimes that's kind of all you can really do is fight and just didn't go my way today."
Elsewhere on Friday, No. 2-seeded Aryna Sabalenka is into the second week of play, and on the verge of a career breakthrough. The hard-hitting Belarusian beat qualifier Maria 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," Serrano said. "I couldn't close it.''
Sabalenka next faces No. 18 Elena Rybakina, who eliminated American Shelby Rogers 6-1, 6-4. Also still in contention is No. 7-seeded Iga Swiatek, the 2020 French Open champion, who breezed into the fourth round by beating Irina-Camelia Begu 6-1, 6-0. Swiatek 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. 21 Ons Jabeur vomited next to the backstop before her first match point and then finished off former Wimbledon champion Garbine Muguruza 5-7, 6-3, 6-2. Jabeur became the first Tunisian woman to reach the fourth round at Wimbledon.
She also had the shot of the day when she hit a running forehand around the net post from off the court for a winner.
American Madison Keys advanced by beating No. 13-seeded Elise Mertens 7-5, 6-3. Keys, seeded 23rd, hit 29 winners to nine for Mertens. The victory was her third this year against a top-20 foe. On Monday, Keys will face Viktorija Golubic.
ESPN's Kathleen McNamee contributed to this report.