Novak beat Benoit Paire 6-3, 6-3 to clinch the win after Filip Krajinovic beat Jo-Wilfried Tsonga 7-5, 7-6. Viktor Troicki/Janko Tipsarevic face Pierre-Hugues Herbert/Nicolas Mahut in the remaining doubles dead rubber.
Serbia will next play against France in away tie on September 15-17. It will be a rematch of the 2010 final when Serbia won their maiden title.
World no.1 Novak Djokovic returns to the tennis court on Friday, as Serbia hosts Kazakhstan in the Davis Cup first round tie in Belgrade.