The Australian Open champion took two hours and 13 minutes to see off the challenge of world number 32 Rybarikova to win 6-1 5-7 6-2.
Li will now face qualifier Petra Cetkovska after she beat Zhang Shuai 6-3 4-6 6-3.
Third seed Petra Kvitova battled into the third round after she claimed victory in a third set tie-break to defeat Venus Williams.
Kvitova eased through the first set before the American hit back, but the Czech player won the battle of the former Wimbledon champions to record a 6-2 2-6 7-6 (9/7) victory.
Eighth seed Caroline Wozniacki was knocked out 6-4 7-5 by Yanina Wickmayer while Angelique Kerber beat Karolina Pliskova 7-6 (7/2) 6-4.
Fourth seed Sara Errani eased into the third round with a comfortable 6-0 6-4 win over Hsieh Su-Wei, while Jana Cepelova beat Samantha Stosur, Monica Niculescu claimed a win against American Bethanie Mattek-Sands and Simona Halep defeated Kaia Kanepi.
In the other games, Ana Ivanovic was defeated 4-6 6-1 6-3 by Klara Zakopalova, while Lucia Sarafova, Jelena Jankovic, Mirjana Lucic-Baroni, Alisa Kleybanova and Annika Beck also progressed.
In the final match of the day, second seed Agnieszka Radwanska beat Sorana Cirstea 7-5 6-0 and will face Lucic-Baroni in the third round.