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.