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Ferrer, the world No 5 and Spain's No 1, outplayed the 37th-ranked Stepanek on the hardcourt of Prague's O2 Arena in two hours and 58 minutes.
"I played very well all the match. I'm very happy with my game," the 30-year-old Ferrer said just after the rubber.
"I was lucky because in the important moments I played better than Radek," he added after winning the seventh out of ten rubbers against Stepanek.
With five double faults and first-serve percentage just over 50 per cent, Stepanek said "the biggest difference was in the serve."
"I wanted to put him under pressure with high percentage of the first serve, coming to the net, taking the activity, changing the rhythm."
"But I played lots of points from the second serve and then his part of the game was more efficient than mine," added Stepanek, 33.
Before the rubber, Ferrer predicted a close game recalling a five-setter they played in the 2009 Davis Cup finals when he finally helped Spain thrash the Czechs 5-0.
But Stepanek, the Czech No 2 player, offered little resistance.
In the first set, Stepanek came back from 0-40 through 11 deuces in game six but then lost his serve two games later.
Ferrer then took the second set with two breaks against Stepanek's one, before completing the job after converting his second match point following another two breaks in the last set.
"We're 1-0 up, but we haven't finished the tie, it's a very long one," said Ferrer.
Despite concerns about a very fast court prepared by the hosts, Ferrer said he felt comfortable.
"It was very fast but I received very well and this maybe was the key," he added.
The Czech Republic's Tomas Berdych will now take on Spain's No 2 player Nicolas Almagro.
"It was very important to win the first point because now Nico can play more quietly," said Ferrer.
On Saturday, Stepanek is likely to team up with Berdych to face Spain's ATP World Finals winners Marcel Granollers and Marc Lopez in the doubles rubber.
"I'll have a rest, support Tomas and be ready for tomorrow," said Stepanek.
"I'll have to save every bit of energy, I'll need it during the weekend," he added.
Spain are missing world No 4 Rafael Nadal, sidelined with a knee injury.
They are looking to add a fourth crown to their three Davis Cup trophies from the last four years, after having won the cup in 2000 and 2004.
Czechoslovakia, which split peacefully into the Czech Republic and Slovakia in 1993, won the Davis Cup in 1980.
But if the Czechs win the 100th edition of the Davis Cup finals, they will clinch a rare team double, last achieved by the United States in 1990, after their women's team lifted the Fed Cup here two weeks ago.
