The Czech next meets 2009 winner Marcos Baghdatis of Cyprus who defeated Gilles Muller 7-6 (5) 4-6 6-3 in an error-strewn clash during which the eighth seed from Luxembourg smashed his racket in frustration.
In a repeat of last year's final, Berdych gained the upper hand against Dimitrov when he broke serve in the 11th game of the first set.
World number five Berdych survived a late scare in the final game of the match, saving a break point before a couple of booming serves put the contest out of reach.
Earlier, 23-year-old American Jack Sock upset third-seeded Frenchman Gilles Simon 7-5 7-6 (5).
His semi-final opponent on Saturday is another Frenchman, second seed Richard Gasquet, who overcame compatriot Jeremy Chardy 2-6 6-3 7-6 (4).
(Editing by Tony Jimenez)
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