"I was dreaming about it my whole life and now we're standing here as Davis Cup champions, it's amazing," said Stepanek after clinching the 100th Davis Cup final.
His success delighted a home crowd that had earlier been silenced when Spain's world number five David Ferrer cruised to a 6-2 6-3 7-5 win over Tomas Berdych to level the final at 2-2 after the Czechs won a four-set doubles rubber on Saturday.
Ferrer's victory over sixth-ranked Berdych put Spain, who have dominated the event in recent seasons but were without injured former world number one Rafa Nadal, back in the hunt for a fourth Davis Cup crown in five years and sixth overall.
The two Czech players have carried the team since 2007 but lost the only other time the country has appeared in the final - a 5-0 drubbing by Spain in 2009 on the clay courts of Barcelona.
Image: Czech Republic's Radek Stepanek celebrates after he won his Davis Cup finals tennis singles match against Spain's Nicolas Almagro in Prague, Czech Republic, Sunday, Nov. 18, 2012. The Czech Republic won the 2012 Davis Cup trophy by beating Spain 3-2.