The 32-time champion Americans will meet the Canada-France victor in the quarterfinals in April.
On Sunday at Forum Fribourg, Ryan Harrison topped Swiss Michael Lammer 7-6 (7-0), 7-6 (7-4) and Fridays' hero John Isner doused Marco Chiudinelli 6-3, 6-4 in a pair of dead rubbers, as Swiss stars Roger Federer and Stan Wawrinka and top American Mardy Fish were replaced in Day 3's reverse singles.
The U.S., captained by former world No. 1 Jim Courier, clinched the stunning victory here on Saturday when its doubles tandem of Mike Bryan and Mardy Fish defeated a Swiss pairing of Federer and Wawrinka in four sets. Federer and Wawrinka were the Olympic gold medal winners in Beijing four years ago.
Switzerland entered this weekend's tie with Federer anchoring its squad at home on clay. However, the 16-time Grand Slam champion was on the losing end twice in less than 24 hours on Friday and Saturday.
On Friday, Fish gave the Americans the first point by gutting out a five- set win over Wawrinka, before Isner did the unthinkable with one of the greatest upsets in Davis Cup history, as he shocked Federer in four sets.
Isner is best known for playing in the longest-ever Grand Slam match two years ago at Wimbledon.
The Americans are 3-1 all-time against Switzerland. The lone Swiss win in the series came 11 years ago in the only previous matchup in Switzerland.