The Swiss beat Rosol 6-4, 3-6, 6-3 in 96 minutes, firing six aces on his way to a quarterfinal clash against Argentina's Federico Delbonis who beat Andrey Kuznetsov 6-3, 6-4.
"I'm very happy about this victory," said Wawrinka, who knocked Rafael Nadal out of the Italian Open in Rome last week before going on to the semifinals, where he lost to fellow countryman Roger Federer.
"I played well today, I'm feeling well," the Lausanne native said.
"I was a bit less intense during the second set, which makes a big difference against players like him," he said.
"But overall it was a good match."
Wawrinka, ranked ninth in the world, is the star of the Geneva Open, held in the Parc des Eaux-Vives, rather than at the Palexpo exhibition centre where last fall he represented the Swiss team that defeated Italy in the Davis Cup semifinals.