Williams topped Romanian Mihaela Buzarnescu 6-3, 5-7, 6-1 in two hours and three minutes on Court Philippe-Chatrier. The eighth-ranked American edged Buzarnescu 5-0 in aces, 26-25 in winners and converted five of 14 break point opportunities.
"She was playing well and I was playing well," Williams told the Tennis Channel. "I felt like she was just hitting winners and the points were so long. It was kind of fun."
No. 4 Aryna Sabalenka was the highest-ranked women's player to advance Wednesday. She beat fellow Belarusian Aliaksandra Sasnovich in straight sets.
Switzerland's Belinda Bencic suffered the biggest upset of the day. Russian Daria Kasatkina beat the 11th-ranked Bencic in straight sets.
Just seven of the Top 13 women's players remain active in the singles circuit. No. 2 Naomi Osaka, No. 3 Simona Halep and No. 12 Petra Kvitova withdrew. No. 7 Bianca Andreescu and No. 13 Garbine Muguruza joined Bencic with early upset losses.
Collins advanced to the third round with a straight-sets win over Ukrainian Anhelina Kalinina. Fellow American Madison Keys also advanced Wednesday with a straight-sets win over Canada's Leylah Fernandez.
Tsitsipas was one of the top players to advance Wednesday on the men's singles circuit. The No. 5 player from Greece beat Spain's Pedro Martinez 6-4, 6-4, 6-3.
Tsitsipas totaled eight aces, three double faults and 30 errors in the two-hour, 27-minute match. Martinez logged seven double faults, 32 errors and did not score an ace in the loss.
Tsitsipas battles American John Isner in the third round Friday in Paris.
No. 6 Alexander Zverev advanced Wednesday with a straight-sets win over Russian Roman Safiullin. The German faces Serbian Laslo Dere in the third round.
"I think he played a fantastic match," Zverev told reporters. "I'm happy to be through in three sets, but the match definitely wasn't easy."
Isner advanced to his third-round clash with Tsitsipas with a straight-sets victory over Serbian Filip Krajinovic. Reilly Opelka and Marcos Giron were among the other Americans to advance Wednesday at Roland Garros.
Second-round matches air until 6 p.m. EDT Wednesday and from 5 a.m. to 6 p.m. EDT Thursday on the Tennis Channel.