Medvedev shrugged off a first-set loss to American Tommy Paul to rattle off three straight-set victories to continue his longest run at Roland Garros.
The No. 2 seed in the men's singles draw won his first-ever main-draw match on the Paris clay earlier this week and is one of three top-six seeds still alive in the bottom half of the draw.
Williams faced a tough test from Mihaela Buzarnescu, who took the second set off the No. 7 seed thanks to some terrific shot-making.
Williams grabbed control of the match in the final set to secure an all-American matchup with Danielle Collins.
Williams and Collins are two of seven American men and women that advanced to the third round on Wednesday.
Wednesday French Open Results
No. 2 Daniil Medvedev def. Tommy Paul, 3-6, 6-1, 6-4, 6-3
No. 5 Stefanos Tsitsipas def. Pedro Martinesz, 6-3, 6-4, 6-3
No. 6 Alexander Zverev def. Roman Safiullin, 7-6 (4), 6-3, 7-6 (1)
Henri Laaksonen def. No. 11 Roberto Batista Agut, 6-3, 2-6, 6-3, 6-2
No. 12 Pablo Carreno Busta def. Enzo Couacaud, 2-6, 6-3, 6-4, 6-4
No. 15 Casper Ruud def. Kamil Majchrzak, 6-3, 6-2, 6-4
No. 22 Cristian Garin def. Mackenzie McDonald, 4-6, 4-6, 7-6 (7), 6-3, 8-6
Kei Nishikori def. No. 23 Karen Khachanov, 4-6, 6-2, 2-6, 6-4, 6-4
No. 27 Fabio Fognini def. Marton Fucsovics, 7-6 (6), 6-1, 6-2
No. 31 John Isner def. Filip Krajinovic, 7-6 (6), 6-1, 7-6 (5)
No. 32 Reilly Opelka def. Jaume Munar, 6-3, 6-2, 3-6, 7-5
Medvedev's game on clay is getting better by the match.
Of course, any type of victory could be viewed as an upgrade from the Russian's previous trips to Roland Garros.
The No. 2 seed appeared to be headed for an upset loss after the first set that was controlled by Paul, the 52nd-ranked man in the world.
Medvedev flipped the match in his favor through a dominant second set in which he won both of his break-point opportunities and took 10 of the 15 receiving points on Paul's serve.
The second-set performance set the tone for the rest of the match, as Medvedev earned 10 more winners, converted four more break points and had 14 fewer unforced errors.
Medvedev will face another American in the third round. No. 32 seed Reilly Opelka defeated Jaume Munar in four sets.
Opelka, No. 31 seed John Isner, Marcos Giron and Steve Johnson are the four American men in the third round.
Isner also faces a difficult test on Friday, as he faces No. 5 seed Stefanos Tsitsipas, who could be viewed as the favorite to reach the final out of the bottom half of the draw.
Tsitsipas won his second consecutive straight-set victory and he has not been tested much in the first two rounds.
Johnson will take on No. 12 Pablo Carreno Busta, and Giron faces No. 22 Cristian Garin, who outlasted Mackenzie McDonald in a five-set thriller.
Garin's comeback from two sets down started with a 9-7 third-set tiebreak win. He completed the match by winning the final set 8-6. The French Open does not have a final-set tiebreak like other majors have.
No. 11 seed Roberto Batista Agut had the most surprising exit on Wednesday, as he was ousted by Swiss qualifier Henri Laaksonen in four sets.
Laaksonen had never gotten past the second round at Roland Garros before this year. He will play Kei Nishikori in the third round for the chance to take on Alexander Zverev in the fourth round.
No. 3 Aryna Sabalenka def. Aliaksandra Sasnovich, 7-5, 6-3
No. 7 Serena Williams def. Mihaela Buzarnescu, 6-3, 5-7, 6-1
Daria Kasatkina def. No. 10 Belinda Bencic, 6-2, 6-2
No. 15 Victoria Azarenka def. Clara Tauson, 7-5, 6-4
No. 20 Marketa Vondrousova def. Harmony Tan, 6-1, 6-3
No. 21 Elena Rybakina def. Nao Hibino, 6-3, 6-1
No. 23 Madison Keys def. Leylah Fernandez, 6-1, 7-5
Katerina Siniakova def. No. 29 Veronika Kudermetova, 7-6 (7), 5-7, 7-5
No. 31 Anastasia Pavlyuchenkova def. Alja Tomljanovic, 6-2, 6-3
No. 33 Paula Badosa def. Danka Kovinic, 6-2, 6-0
Even though Williams dropped a set on Wednesday, she is still viewed as one of the favorites to come out of the bottom half of the women's singles draw.
The No. 7 seed had a tough time putting away Buzarnescu because the 33-year-old Romanian made a handful of terrific shots in clutch situations.
In fact, Buzarnescu finished with one fewer winner than Williams for the entire match. She produced 12 winners and a pair of breaks in the second set.
Williams eventually took over in the third set, as she went 3-of-4 on break-point opportunities and won 13 more points than Buzarnescu.
Williams is still on a collision course with No. 3 Aryna Sabalenka for a quarterfinal showdown. The two women are the only top 10 seeds left in their half of the draw.
Belinda Bencic was the latest top-10 player to exit that section, as she fell in straight sets to Daria Kasatkina.
Bencic's loss guaranteed the appearance of one unseeded player in the quarterfinal. Bianca Andreescu and Johanna Konta were upset in the first round, while Bencic and Veronika Kudermetova lost on Wednesday.
Marketa Vondrousova and Paula Badosa are the only seeds left in the bottom two sections. They both won in straight sets to qualify for the third round.
If both of those players lose in the third round, the women's draw will have two unseeded quarterfinalists and one will make the semifinals to potentially play Williams or Sabalenka.
Statistics obtained from RolandGarros.com.