After falling an early break behind, Cornet took charge of the match with a run of eight uninterrupted games. However, from this commanding position, her grip on proceedings slipped somewhat, enabling a clinical Kucova to hit back and force a decider.
In recent years, Cornet has earned herself a reputation as the WTA's marathon woman due to her involvement in a succession of epic three-setters. She drew on all of this experience against Kucova, upping her game to win the final four games and wrap up a 63 46 63 win.
"She played very well today and the fast surface suits her game," Cornet said. "It was a very tough match for me, I was 63 31 up and she started playing better and I was too far from the baseline.
"But in the third set I changed a few things and I was happy I saved quite a few break points and I managed to win in the end!"
Next, Cornet, who accepted a late wildcard into the draw, will play the in-form Klara Koukalova.
"Koukalova is in very good shape right now, she has won a lot of matches this year and a title. For sure it´s going to be a good match and a good fight. It's a great preparation for Fed Cup for me, it's a bonus for me to be here," Cornet added.
Despite a slight lapse at the start of the second set, No.6 seed Meusburger proved far too solid for Lucic-Baroni, winning 62 63, while Rybarikova, the No.7 seed, was even more dominant, taking a mere 58 minutes to brush aside Soler-Espinosa, 62 60.
"I think that I played a perfect match today. I was actually surprised with how I played coming from Monterrey and with the jet lag and all," Rybarikova said. "But I am very satisfied with my performance. My next opponent is going to be very tough so I will have to really play my best to win the match."