Michael Lammer and world number 10 Stanislas Wawrinka gave the home team a 3-0 lead on Saturday by beating Ecuadorians Emilio Gomez and Roberto Quiroz 6-3, 6-4, 3-6, 6-7 (7), 6-4 in doubles play.
Wawrinka, who came close to toppling world number one Novak Djokovic in the semifinals of the US Open, acknowledged his “batteries were dead” after the three hour, 35-minute match.
The Lausanne native plans to take a week off before resuming competition in Kuala Lumpur.
Roger Federer, the world number six player, did not play for the Swiss team and it remains an open question whether he will participate next year.
Spain, the Netherlands, Australia, Britain, Germany, Belgium and Japan were among other nations qualifying for the Davis Cup 2014 world group over the weekend.
Rafael Nadal, recent winner of the US Open, and Marc Lopez joining forces for the Spanish side to beat Denys Moichanov and Sergly Stakhovsky of the Ukraine in four sets.
A draw is set for Wednesday to determine who Switzerland and the other qualifying nations will play in the world play-offs.
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In other action over the weekend, Serbia, aided by Djokovic, defeated Canada 3-2 in Belgrade to enter the 2013 Davis Cup final against the Czech Republic, which beat Argentina 3-2 at Prague.
The final is set for Serbia in November.