"Kristyna played really, really well", said Williams, who returned to tennis at Indian Wells in March, six months after giving birth to her first child.
There was a little rust to shake off on her return but all the same Serena was too strong, and too good, for her world 70-ranked opponent to set up a meeting with Australia's Ashleigh Barty in the next round.
Williams hasn't played in a while, so her world ranking has dropped a lot.
Canadian teen Denis Shapovalov's first Grand Slam match as a seeded player went about as smoothly as could be.
The 36-year-old got off to a winning start in straight sets over Kristyna Pliskova.
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"I don't know how many aces there were", Serena smiled courtside after the match.
"All the mums out there that had a tough pregnancy and have to come back and try to be fierce, in a middle of everything", she told journalist Jon Wertheim, "that's what this represents".
Williams built a 2-1 lead in the opening set on the strength of her serve. Pliskova, who hit 10 aces, loses set with a wild forehand. She watches every single tennis match she possibly can, scheduling her limited vacation times around tournaments just to be able to watch every match.
The Russian appeared to be cruising at 6-1 3-1 ahead but Holland's Richel Hogenkamp suddenly had her on the ropes, taking the second set and racing 3-0 ahead in the decider. She had 29 winners and 25 unforced errors.
Making her eighth main draw appearance at Roland Garros (and ninth appearance overall), after her maiden major quarter-final reached a year ago, Garcia salvaged a slim chance of ascending to World No.1 this fortnight: she would need to win the title with Wozniacki not reaching R16, Halep losing before the semis and Muguruza going out before the final. Garcia, who celebrated her 28th major match win, will face Shuai Peng who beat 6-3 6-4 Aleksandra Krunic in her first WTA victory of the season. It is the first break of the match.