The world number two, and recently-crowned ATP World Tour Finals champion, beat 44th-ranked veteran Stepanek 7-5, 6-1, 6-4 in two hours and 10 minutes. "The 1-0 lead is very important for us," the 26-year-old Djokovic told a frantic crowd in the sold-out Belgrade Arena sitting 15,500 people.
Relying on a solid first serve throughout the rubber, Djokovic broke Stepanek's serve in game six of the first set. But then he found himself under heavy pressure, allowing the 34-year-old Czech to win seven straight points at one moment and take the serve back.
Djokovic showed some frustration before breaking Stepanek again for a 7-5 first-set win. Stepanek earned three break points early in the second set, but Djokovic held on to his serve and embarked on a spree to take the set, 6-1.
A single break in game nine was all Djokovic needed in the third set to finish off Stepanek. "I am happy with the way I played. Of course I was nervous at the beginning but it was very important for us to win the first set and then I relaxed," he said. "I served well in the important moments."
Serbia's world number 117 Dusan Lajovic will now take on seventh-ranked Tomas Berdych in the second rubber of the day. Serbia won their only Davis Cup final so far in 2010. The Czech Republic, who won in 2012, are playing their third final in five years.