Thiem, who reached last year's final, saved two set points in the fourth set before clinching it 7-5.
Stephens blew four match points in the second before eventually hanging on in three to put away Polona Hercog 6-3, 5-7, 6-4.
- Djokovic eased through his opener in straight sets against Poland's Hubert Hurkacz as he bids to become only the second man to hold all four Slams simultaneously for a second time.
"The first set I got rolled", she said.
"Today I kind of felt like a challenger".
Since those early-for-her defeats, Williams had won six of the 14 majors she entered to surpass Steffi Graf's professional-era record of 22 Grand Slam singles championships. "I'm really happy I could fight until the end and win this hard match". "So in those moments, she's been a lot in those situations where those margins are really small".
Naomi Osaka continued to live dangerously at the French Open but her hopes of a third successive grand slam title remain intact after a comeback win against Victoria Azarenka.
Azarenka threw everything at Osaka in the opening game of the decider as she tried to wrestle back the initiative, carving out three break points, but she could not convert any of them. That kind of just relaxed me.
"It was an unfortunate second round draw for me so I am happy to win".
Azarenka, now ranked No. 43 and without a major title since winning the Australian Open in 2012 and 2013, raced to a 4-0 lead on Court Suzanne Lenglen and kept Osaka under constant pressure.
Defending champion Simona Halep looked headed for a relatively straightforward, straight-set victory in the French Open's second round - until everything started to fall apart for her.
"I played as much as I need to play to win in straight sets", the 15-times Grand Slam champion said. Thiem topped Alexander Bublik of Kazakhstan 6-3, 6-7 (6), 6-3, 7-5; Fognini got by Federico Delbonis of Argentina 6-4, 3-6, 6-3, 6-3; and Khachanov beat wild card Gregoire Barrere of France 6-3, 7-6 (6), 0-6, 7-5.
Viktoria Kuzmova (Svk) bt Kiki Bertens (Ned) 3-1 retd.; 26-Johanna Konta (Grb) bt Lauren Davis (USA) 6-3, 1-6, 6-3; 23-Donna Vekic (Cro) bt Rebecca Peterson (Swe) 1-6, 6-1, 6-2.
Osaka never made it past the third round in three previous Roland Garros appearances.
Serena Williams moved smoothly through to the third round with a 6-3 6-2 defeat of Japanese qualifier Kurumi Nara, setting up an all-American tussle with Sofia Kenin who benefited from the withdrawal of 22nd seed Bianca Andreescu through injury. It doesn't make you a better or worse player.
"She played really well and aggressive, and could attack my balls", admitted Wang, adding that her 17-year-old opponent has the prospect of reaching top 10 on ranking if she keeps playing like that.