Janko Tipsarevic and Viktor Troicki won all four points for their team and booked a ticket to the semifinals for the defending champions.
Serbia is now one step closer to retaining their Davis Cup by BNP Paribas trophy.
The full results are listed below:
R1: Victor Troicki (SRB) d. Michael Ryderstedt (SWE) 3-6 1-6 7-6(6) 5-7
R2: Janko Tipsarevic (SRB) d. Ervin Eleskovi (SWE) 2-6 0-1
R3: Simon Aspelin / Robert Lindstedt (SWE) d. Novak Djokovic / Nenad Zimonjic (RUS) 6-4 7-6(5) 7-5
R4: Janko Tipsarevic (SRB) d Michael Ryderstedt (SWE) 2-6 5-7 3-6
R5: Victor Troicki (SRB) d. Robert Lindstedt (SWE) 6-3 4-6 0-0