De Bakker battled Berdych for more than 2 hours before finishing a 7-5, 7-5 victory. He had three breaks in the first set and the lone break in the second to beat Berdych for the first time in his career.
Berdych managed 12 break opportunities but de Bakker was able to fight off 10 of them, including all three he saw in the second set.
All four quarterfinals Friday ended in upset wins as second-seeded Nicolas Almagro and No. 3 Juan Monaco were also beaten. Carlos Berlocq defeated a higher-ranked Albert Ramos in a match between unseeded players.
Fernando Verdasco, the No. 8-seed, took out Almagro 6-4, 4-6, 7-5, using a pair of third-set breaks to move into the semifinals.
Fifth-seeded Grigor Dimitrov raced by Monaco 6-3, 6-2 in 65 minutes. Dimitrov ended with five breaks as he won more than half the points off Monaco's serve.
Berlocq outlasted Ramos 6-3, 3-6, 6-0, taking two-thirds of the points in the third set.
Dimitrov and Verdasco meet in the first of Saturday's semifinals. It will be their first meeting in an ATP event. De Bakker and Berlocq also have never played each other before.