Stepanek dispatched Lajovic 6-3, 6-1, 6-1 to hand defending champs their second straight Davis Cup title after beating Spain in last year's championship tilt.
The 34-year-old Czech veteran needed 1 hour, 52 minutes to overcome his 23-year-old opponent, breaking him seven times in the one-sided match.
Lajovic was playing due to an injury to former Top 10 star Janko Tipsarevic.
The Czechs are the first repeat Davis Cup champs since Spain in 2008-09.
The fifth rubber was necessitated when world No. 2 Novak Djokovic kept Serbia's hopes alive in Sunday's first reverse-singles match by topping world No. 7 Tomas Berdych 6-4, 7-6 (7-5), 6-2 at Belgrade's Kombank Arena.
The Czech Republic came into Sunday's action with a 2-1 lead thanks to a straight-set victory by the doubles tandem of Berdych and Stepanek over the Serbian duo of Nenad Zimonjic and Ilija Bozoljac Saturday.
Dog comes home gnawing on human bone
Julius Randle breaks leg during NBA debut