The top-seeded Williams dictated most points and wound up with 30 more winners — but also 24 more unforced errors — than Lim.
Williams is a 17-time major champion who was facing a woman making her Grand Slam debut. Still, there was a bit of shakiness from the 32-year-old American as she served out the final game, erasing four break points and needing five match points to close things. Williams saved all seven break points she faced in the match.
She improved to 54-1 in first-round matches at majors. The only loss came at the 2012 French Open against 111th-ranked Virginie Razzano.
Venus Williams was also playing, and winning. The older Williams sibling defeated Belinda Bencic, 6-4, 6-1.
The Williams sister could meet in the third round if both get through their next matches.
Roger Federer had little trouble beating Lukas Lacko of Slovakia, 6-2, 6-4, 6-2.
The French Open is only Federer's third clay-court tournament this season. He reached the final in Monte Carlo but missed the Madrid tournament when his second set of twins, boys Leo and Lenny, was born.
His first match after their birth was a loss in Rome.
On Sunday, with the clay court hard and damp due to days of rain and overcast skies, the fourth-seeded Federer was back to himself, winning five of his 11 break points.
"I was happy seeing, getting early signs out of the match that I was actually playing well and I was going to get my chances I was looking for," Federer said. "My personal life, as we know, it's all great, so I'm happy the family is here."
Eighth-seeded Milos Raonic of Canada also advanced, beating Nick Kyrgios of Australia, 6-3, 7-6 (1), 6-3.
Raonic is the youngest man in the top 10 of the tennis rankings, and Kyrgios was the youngest man in this year's French Open draw at 19.
"I was a bit nervous going out in the first set. That's normal, I think," said Kyrgios, a former top-ranked junior player who won the junior Australian Open in 2013.
Tenth-seeded John Isner hit 23 aces and got the only break of serve he needed in the third set of a 7-6 (5), 7-6 (4), 7-5 victory over 130th-ranked Pierre-Hugues Herbert
Also, Agnieszka Radwanska was able to reach the second round — once she got a handle on her serve.
Radwanska and Zhang Shuai traded breaks in the opening seven games of their match, but the third-seeded Pole finally held and won the final nine games to become the first player to reach the second round, winning 6-3, 6-0.
No. 14 Carla Suarez Navarro of Spain and 31 Daniela Hantuchova of Slovakia also advanced in the women's draw.