Ferrer, the world number five, needed just two hours and 25 minutes to see off sixth-ranked Berdych 6-2, 6-3, 7-5 on the hardcourt of Prague's O2 Arena.
The Czech Republic's Radek Stepanek, the world number 37, will now take on Spain's 11th-ranked Nicolas Almagro in the decisive rubber.
Berdych, who played a four-hour five-setter on Friday and the doubles rubber on Saturday, got off to a slow start against Ferrer.
The 27-year-old Czech lost his very first serve in the first set and then another to let Ferrer, 30, get ahead without too much trouble.
"He (Berdych) played a lot of matches, he played five sets with Nicolas and four sets yesterday," said Ferrer.
"I played very focused, very aggressive, I started really good and maybe that was the key," he added, praising his first serve and forehand.
Ferrer broke Berdych's serve early in the second set for a 3-0 lead that prompted Berdych to take a bathroom break.
But even that did not help, Berdych was flat and allowed Ferrer to gain the upper hand in long exchanges and finally take the second set too.
In the third set, Berdych managed to come back from 4-2 down but the home crowd of more than 14,000 people did not cheer long as Ferrer broke him again to win the rubber.
On Friday, Ferrer beat Stepanek 6-3, 6-4, 6-4 and Berdych then put the Czechs level after beating Almagro 6-3, 3-6, 6-3, 6-7 (5/7), 6-3.
In Saturday's doubles rubber, Berdych and Stepanek beat Marcel Granollers and Marc Lopez 3-6, 7-5, 7-5, 6-3 for their 12th victory in Davis Cup doubles against a single loss.
Spain are missing world number four Rafael Nadal, who is recovering from a knee injury.
They are looking to win the Davis Cup for the fourth time in five years, in addition to trophies won in 2000 and 2004.
The Czech Republic is eyeing the first trophy since becoming an independent country after a 1993 split with Slovakia.
Former Czechoslovakia won the Davis Cup in 1980.