In contrast to her fortunes on the clay in Strasbourg, Cornet has struggled to find her best tennis in the French capital in recent years, suffering a string of premature exits at both the Stade Pierre de Coubertin and up the road at Roland Garros.
Against Rybarikova, there were her usual flashes of brilliance, although this was accompanied by the odd moment of frustration. In the end a run of three straight games at the start of the deciding set proved the difference, Cornet wrapping up a 63 57 62 victory with a trademark drop shot, much to the delight of the home crowd.
"Playing in front of a French crowd is always amazing," Cornet, who will meet No.2 seed Petra Kvitova next, said. "It doesn't happen so often during the year so I'm really happy to play with my friends and family watching.
"During the tournament, I'm just trying to stay focused and taking each match as it comes."
Despite favoring the slower surfaces on tour, Suárez Navarro was a quarterfinalist here 12 months ago and made a confident start this time around, easing past Johanna Larsson, 61 64. Hantuchova meanwhile looked to be heading for a similarly comfortable win only for her opponent, Marina Erakovic, to retire with a back injury midway through the second set.