The 13th-seeded Verdasco rallied past Olivier Rochus of Belgium 4-6, 6-2, 7-5 and will next play Ivan Dodig of Croatia. The Spaniard dropped serve twice in the first set but didn't face another break point.
"I've got to the final here before, so it's one of my favorite tournaments," said Verdasco, who was crushed 6-0, 6-1 by seven-time champion Rafael Nadal of Spain in the final two years ago.
The 15th-seeded Melzer and Dolgopolov, seeded 16th, had much easier matches.
Dolgopolov defeated Juan Igancio Chela of Argentina 6-2, 6-2, setting up a match against Bernard Tomic of Australia.
The 19-year-old Tomic was happy with how he mixed sliced forehands with heavy groundstrokes in his 6-4, 6-3 win against Denis Istomin of Uzbekistan.
"Regardless of any surface, he's pretty hard to play against," Tomic said. "A lot of clay-court players play behind the line. But I think my tennis is something different. If I play my tennis, they struggle with my game -- even on clay."
"I was happy the way I was moving, and I was keeping the ball in the court," Mathieu said. "I don't have the knees of a 20-year-old anymore. But I'm able to play 100 percent without any problems. Things are improving."
Nadal, the six-time French Open champion, is chasing his first title since winning at Roland Garros last year.
"I have lots of success on clay in the past, so I want to do well here," Nadal said. "I haven't won a title (for 10 months), but how many finals have I played?"
Nadal has lost to Novak Djokovic in seven consecutive finals, and he could face the top-ranked Serb in the final. Djokovic is scheduled to play against Italy's Andreas Seppi or Romania's Victor Hanescu.