Berdych, the number 16 who eliminated top seed Roger Federer in the previous round, struggled in the opening set but came out on top in the tiebreak in the second and produced an aggressive display in the deciding third set.
After another impressive win, Berdych will be confident of getting through to Sunday's final. Andy Roddick and Rafa Nadal will meet in Friday's first semi-final.
"The start was quite slow for me because I was still feeling a little bit tired after the long, long match against Roger that finished late in the night," Berdych said.
"But then finally I found my rhythm, started to play really well and I think the beginning of the third set Fernando was struggling a bit and maybe he was maybe a little bit tired -- that was my advantage. I'm very happy that I used it and got through," he added.
The Czech broke with a superb backhand crosscourt pass in the seventh game of the final set and from that point there was little doubt about the outcome, with 10th seed Verdasco blasting the ball but lacking control.
"I was feeling that I can play the long rallies so I was just trying to keep the ball in play as long as I could and just to give him the chance to make an error -- most of the time that worked," he said.
Berdych next faces Soderling, who scored a 6-1, 6-4 win over Russian Mikhail Youzhny.
The fifth-seeded Swede suffered a break on his first serve but recovered in splendid fashion to win the next six games.
Neither player could establish control on serve in the second set, with the first three games all going against serve, but Soderling did enough to run out a comfortable winner in the end.
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