Rybakina saw off experienced Shelby Rogers of the United States 4-6, 6-1, 6-2 in front of the watching Roger Federer, the retired eight-time champion who was a special guest in the royal box.
The 24-year-old Kazakh arrived in London under a cloud after struggling with a virus which saw her suffer an early loss in Berlin before pulling out of Eastbourne.
"I'm feeling much better although it wasn't easy to get back to fitness," said Rybakina.
"I'm happy to get the win and it gives more confidence for the next round."
Rogers, 31, had defeated Rybakina on grass at Hertogenbosch last year and initially she was in charge again under the roof of Centre Court as the All England Club was deluged by torrential rain.
The champion double-faulted on the first point on her way to being broken.
That was enough to give the 49th-ranked Rogers the foundation to claim the opening set.
Suddenly, Rybakina was looking at becoming the first defending champion to lose in the opening round since Steffi Graf was beaten by Lori McNeil in 1994.
However, she steadied the ship, racing into a 5-0 lead in the second set before levelling the tie.
A double break in the decider then set her comfortably on her way to victory and a second round clash with either Alize Cornet of France or Japan's Nao Hibino.
