Rybakina, who won Wimbledon in 2022, is looking to clinch her second Grand Slam crown this year after her triumph at the Australian Open in January.
The 27-year-old is also in contention to take top spot in the WTA rankings from Aryna Sabalenka depending on their results at the All England Club over the next fortnight.
"It was a really difficult match, also not coming from too many wins. I had to really fight," said the reigning Australian Open champion, who hit 13 unforced errors in the second set on Court One after 12 in the first and 10 more in the third.
"I need to improve quite a lot, but I'm happy to get another opportunity."
"My serve percentage wasn't the greatest so when she was getting good first serves in, it wasn't easy to break her," said Rybakina, who talked to her coaching team during the medical timeout.
"They were just trying to tell me to keep on going, bring the energy, better footwork and I'm glad I managed."
With her victory, Rybakina will now face Caty McNally or Elena-Gabriela Ruse in the second round.