Berdych and Stepanek combined to win the doubles on Saturday, after Ferrer had accounted for the world number 31, while Berdych had got the better of Almagro earlier in the weekend.
Czech Republic beat world heavyweights Argentina, Serbia and Italy on their way to the final and hailed a remarkable achievement.
There are no words to say. Undescribable. This is the best thing that can be, Berdych said.
Hero Stepanek said it was “history made” and something he’d long dreamed about.
“We’ve been dreaming about it since the series against Switzerland,” Stepanek said. “Whatever it takes in the Davis Cup, we’ll go through it.”