The Serbs outlasted the Russians 6-3, 7-6 (8-6), 7-6 (7-5). Despite two tiebreakers in the 2-hour, 37-minute match, the Serbians prevailed after their service was broken just once and 10 aces on their own serve.
Djokovic, the reigning Australian Open champion, returned from a bout with the flu to help his nation stay alive in this year's cup quarterfinals.
In Sunday's reverse singles, Djokovic faces Nikolay Davydenko and Viktor Troicki will play Mikhail Youzhny.
In other matchups, Israel has a 2-1 advantage against Sweden; the United States has an insurmountable 3-0 lead over Austria; Belgium leads the Czech Republic 3-0; Spain leads Peru 2-0; France leads Romania 3-0; Argentina has a 3-0 lead against England; and Germany leads the Korean Republic 2-1.