Simon saved four set points in the 10th game of the first set and was down 5-3 in the tiebreaker before winning the next four points, clinching it when Berdych sent a forehand into the net.
But Berdych took a 3-0 lead in the second and broke his opponent in the 11th game of the decider. He was down 0-40 in the next game before serving out the match to reach his third final of the year.
"With Gilles you know it's going to be long, as it's his game," Berdych said. "He likes to play long rallies, and I was trying to deal with that today, the last game was very long, very tough, but my serves helped me to finish it."
The hard-serving Raonic hit 23 aces in the second semifinal but struggled with unforced errors in the first set. In the second, he broke Gasquet in the 12th game to level the match and earned another break in the last game of the decider.
It was another tight match between the two, after Raonic wasted a match point before losing to Gasquet in five sets in the fourth round of the U.S. Open.
"He was playing really well," Raonic said. "He didn't make a lot of errors. I just said to myself I had to focus on my first serves."