Bozoljac and Zimonjic surprised the American brother tandem of Mike and Bob Bryan, giving Serbia a 2-1 lead in the best-of-five match series.
With world No. 1 Novak Djokovic set to play in one of Sunday's two remaining singles matches, Serbia became a clear favorite to win the quarterfinal series. Djokovic will meet Sam Querrey, after which American John Isner will face Viktor Troicki.
The doubles match was an obvious critical juncture in the Serbia-United States matchup and the Americans were favored since the Bryans are the No. 1 ranked doubles team in the world.
Bozoljac and Zimonjic prevailed, however, 7-6 (7-5), 7-6 (7-1), 5-7, 4-6, 15-13.
The match lasted 4 hours, 23 minutes with the final set taking 1 hour, 39 minutes to complete. There were 434 points played and they were split exactly in half.
There were 36 aces served by the Serbian team to 12 for the Americans.
The Bryans also lost their match in the opening round of this year's Davis Cup competition, but the United States survived on that occasion to defeat Brazil 3-2.