The all important point was delivered by the Swiss pairing of Marco Chiudinelli and Michael Lanmer, who saw off Nenad Zimonjic and Filip Krajinovic 6-6 (7/3), 3-6, 6-6 (7/2), 6-2.
The Swiss took control of the tie in Novi Sad when Roger Federer, yet to add the Davis Cup trophy to his array of silverware, and freshly crowned Australian champion Stanislas Wawrinka, won both of their singles.
Federer, a last minute addition to the team, beat 268th-ranked Ilija Bozoljar in three sets, with Wawrinka, the new world number three, needing four sets to dispatch 102nd ranked Dusan Lajovic.
Serbia, the 2010 winners, were up against it with their side weakened by the absence of Novak Djokovic and Janko Tipsarevic.
The winner will face either Kazakhstan or Belgium who are playing in Astana, with the hosts leading 2-1.