Troicki and Zimonjic defeated Belgians Ruben Bemelmans and Steve Darcis 6-4, 6-4, 5-7, 6-4, giving Serbia a 3-0 lead in the best-of-five series. The Serbs head to the April 5-7 quarterfinals against either Croatia or Italy, who were tied 1-1 after Friday's play.
It was the second point of the series for Troicki, who opened play Friday by rallying back from a two-set, one-break deficit late to beat David Goffin. World No. 1 Novak Djokovic put Serbia up 2-0 with a 6-3, 6-2, 6-2 win over Olivier Rochus.
Troicki and Zimonjic had the lone break in the first set and needed two to take the second. Bemelmans and Darcis kept the match going with a late third-set break but the Serbs finished the match and locked up the series with a break -- their fourth of the day -- in the final game.
Both sides had 29 unforced errors but Troicki and Zimonjic combined for 91 winners and took 82 percent of the points on serve.
Sunday's schedule called for Djokovic to meet Goffin and Troicki to get against Rochus in the reverse singles.