Gauff is living up to her career-best ranking of No. 25, advancing by beating Qiang Wang 6-3, 7-6 (1). Gauff earned her first clay-court final when she beat Wang in Parma, Italy, less than two weeks ago.
Gauff has 23 match victories this season, and only three women have more. She won the girls' singles title at Roland Garros three years ago.
2017 US Open champion Stephens beat a top-10 player for the first time in 2½ years to reach the third round.
Stephens returned well and used her defensive skills to defuse 10th-ranked Karolina Pliskova's power for a 7-5, 6-1 victory.
The steady Stephens had 22 winners and only 17 unforced errors, and she broke six times.
Ranked 59th, Stephens is out of the top 50 for the first time since 2017 but always dangerous on clay. She was the runner-up at the 2018 French Open and made the quarterfinals in 2019.
After ending a four-match losing streak on clay in the previous round, last year's runner-up Kenin advanced to the third round with a 7-5, 6-3 win over Hailey Baptiste in a battle of Americans.
Kenin has had a tough start to the season. The 2020 Australian Open champion underwent an emergency appendectomy in Melbourne in February, and her record was 7-8 entering the clay-court Grand Slam.
Svitolina played brilliantly in the opening set by combining deep shots from the baseline with clever play at the net and dropping only five points on her service games. She recovered from a blip early in the second set to win the last five games.
Information from The Associated Press was used in this report.