Rybarikova and Schiavone played an absolute grinder, battling for three hours on Centre Court before the Slovak won four points in a row from 3-all in the third set tie-break to end it, 75 46 76(3).
"It was a very tough match today," Rybarikova said. "Not only does Francesca have a tricky game, but it was pretty windy out there, and the temperature kept changing too - it was hot at the beginning but then it got colder as the match went on. I'm just happy I could make the second round today."
Awaiting Rybarikova in the second round is none other than Li, not just the 2011 French Open champion but now a two-time Grand Slam champion, having won the Australian Open a few weeks ago. There's even more - Li is 12-0 this year, the No.1 seed here and days away from rising to No.2.
"It's going to be another tough match for me, for sure," Rybarikova said. "She's playing very good tennis and has a lot of confidence right now. I played her a few years ago and won that match, but it was on a different surface - grass - and it's totally different now. I have to play my best to win."
That match Rybarikova remembered was actually their only previous meeting - it came in the final of Birmingham in 2009, and Rybarikova won in staight sets. Li was ranked No.20 at the time though.
Speaking of Li, she talked about what she's been up to since Melbourne in her pre-tournament presser.
"There wasn't much celebration really, because after Melbourne I went back to China and it was the Chinese New Year. So I enjoyed myself, with my parents and my friends, and after that I was back to the gym and went to see the doctor too, just to make sure everything was good, and then came here."
And now that it's been a few weeks since she conquered the Australian Open, Li talked about the differences between winning her first Grand Slam three years ago and winning her second one now.
"It's much different," she said. "When I won the first one it was more exciting, because I didn't know what was happening - I didn't know what would happen if I won, and I didn't know what would happen if I lost. But the second one was much different. I was training so hard, not just technique but also mentally. I was working so hard these one and a half years to prepare to win another one.
"So this time it wasn't as exciting as the first one - I was much more relaxed, more calm."
Next Monday, regardless of what happens this week, Li will rise to No.2 in the world, raising the bar on her own record of No.3 for highest-ranked Asian player, male or female, in the history of tennis.
"Everyone would like to have a higher ranking, right?" Li said. "I was really happy to hear about that. But next week is next week. I still have to prepare for what I'm doing here in Doha this week.
"I have to play well here."