Home favourite Simon won three straight games in the middle stages of the first set to move into a 4-2 lead over the world number six.
The two players then exchanged games before Simon was given the opportunity to serve for the set, which he did successfully at the first attempt.
Berdych raced into a 3-0 advantage in the second after gaining a break courtesy of a couple of unforced errors from Simon.
Urged on by his native crowd, Simon fought back to claim consecutive breaks of his own, turning the scores around to 5-4.
Despite saving one match point, Czech Berdych could not prevent Simon's momentum taking him over the line as the world number 20 secured victory in an hour and 45 minutes.