The No.5-seeded Koukalova rallied from a set and a break down to beat Annika Beck in a few minutes shy of two hours, 46 63 61. From 1-0 down in the third she won six games in a row to close it out.
"It took me a while to find my rhythm but Annika is a very tough opponent," Koukalova said of Beck, one of the tour's most promising rising stars. "She's just a few spots behind me in the rankings.
"It was a tough match and I was very happy to improve my game in the third set."
Koukalova is now the third player so far this year to reach 20 WTA-level match wins, after Li (who has 21) and Cibulkova (who has 20). Agnieszka Radwanska will try to reach 20 herself on Thursday.
"It feels great - I didn't know that I've won 20 matches this year now," Koukalova said afterwards. "It's a positive thing that I've won so many matches this year. It definitely gives me a lot of confidence."
There was only one more second round match in the day session and it saw Shahar Peer upset No.8 seed Tsvetana Pironkova, 62 61. It was an upset on paper but not if you look at the head-to-head - Peer had won four of the pair's last five meetings, including in the first round in Katowice last year.
The other daytime matches were both first rounds, with No.7 seed Magdalena Rybarikova beating French qualifier Claire Feuerstein, 62 75, and Mirjana Lucic-Baroni beating Jovana Jaksic, 63 64. Jaksic was coming off a breakthrough week, reaching the first WTA final of her career in Monterrey.
"It was a very tough match, physically and mentally," Suárez Navarro said. "Cadantu is a big fighter. I really had to stay in every point and not give any free points away. It was important not to lose focus and I hung in there as much as I could. And I'm really happy that I got through this match.
"Now I'll have a day off, which will help me recover physically."
Giorgi's win over the No.16-ranked Vinci was the seventh Top 20 win of her career. She has had three Top 10 wins - against Sara Errani, Caroline Wozniacki and Maria Sharapova, and three other wins against players in the No.11-No.20 range - Flavia Pennetta, Nadia Petrova and Marion Bartoli.