Serbia's world number two Novak Djokovic levelled the tie earlier in the day with a straight-sets win over Tomas Berdych, but the passionate home fans were silenced by a cool performance from Stepanek who gave the 117th-ranked Lajovic no chance in the decisive rubber.
Lajovic had 17,000 noisy Serbian fans on their feet when he broke Stepanek in the opening game but it turned out to be the high point of the match for the 23-year-old, as his more experienced opponent highlighted the gulf in class between the two players.
Stepanek combined his baseline and volleying skills to good effect and was mobbed by his team mates when he sealed victory after one hour and 52 minutes.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
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