Tsonga had looked to reach consecutive finals, after winning the Moselle Open last month, but the Frenchman's baseline drives too often went long against Berdych. Despite taking the second set, he seemed to lose focus in the third as Berdych broke him twice to set up the win.
"The chance was here. I'm happy to take this chance to be in the final," said the third-seeded Berdych, who progressed to his first final of the season.
A win on Sunday would be a major boost toward the Czech's hopes of securing one of four remaining spots at the season-ending ATP World Tour Finals in London.
"This match could really change my season from a good season to a really good season," Berdych said.
Cilic, for his part, continued his recent run of good form with a 6-4, 6-3 win over Ivan Ljubicic. The two big-hitting Croats combined for 22 aces.
Winning against the player who beat him in the first round at Wimbledon was a confidence boost, he said.
"That means a lot, that I can beat those guys and my tennis is at a good level and on a level that's high enough to play against those guys and beat them," Cilic said.
Radwanska, the winner of last week's Pan Pacific Open in Tokyo, beat Flavia Pennetta 6-2, 6-4, to improve her career record against the Italian to 3-1.
Petkovic defeated Monica Niculescu 6-2, 6-0.
The Polish player has won her four previous meetings with Petkovic, including twice this year. But Radwanska said she wasn't expecting an easy time Sunday.
"It's always very tough and very tight against Andrea," the 11th-seeded Radwanska said. "She's playing very well, very consistent. I think I'll have to play even better than today to beat her tomorrow."
Petkovic said she drew confidence from her increasingly steady performances, having reached the quarterfinals at each of this year's Australian, French and U.S. Opens. The win marked her first victory in three meetings with Niculescu.
"I was really satisfied with the intensity and the focus I managed to have with each and every point, and I think that made the difference today," she said.