The best-of-five tie came to a close Sunday, with the Spaniards winning a pair of dead rubbers. Nicolas Almagro whipped Evgeny Korolev 6-3, 6-4 and Marcel Granollers got past Andrey Golubev 6-3, 6-7 (2-7), 6-3 in Oviedo.
Spain, which played this week without top-five stars Rafael Nadal and David Ferrer, clinched the victory here on Saturday when Granollers and Marc Lopez leveled a Kazakhstani doubles tandem of Korolev and Yuri Schukin in straight sets.
Nadal had previously stated that he would not play Davis Cup this year.
Former world No. 1 star Juan Carlos Ferrero and Almagro lifted Spain to a commanding 2-0 lead following Friday's opening singles.
The Spaniards, led by rookie captain Alex Corretja this year, have won five of the last 12 Davis Cup championships. They will host Austria in April and haven't lost a home Davis Cup tie since 1999.