The world No. 8 Fish, playing on his worst surface, came from behind to best the 28th-ranked Wawrinka 6-2, 4-6, 4-6, 6-1, 9-7 on red clay at Forum Fribourg. The grueling rubber finally ended after 4 hours, 26 minutes when Fish converted on his third match point with a cross-court volley winner.
Fish, who improved to 7-7 in his career Davis Cup singles, wound up with 15 aces and broke Wawrinka's serve seven times, compared to four breaks for the Swiss loser.
Friday's second opening singles rubber will pit the great Roger Federer against 6-foot-9 American John Isner. This will mark the 16-time Grand Slam champion Federer's first World Group action since 2004, as he has played in only a few playoffs and zonal matchups since then.
Saturday's doubles in Fribourg will pit an American tandem of Mike Bryan and Ryan Harrison against a powerful Swiss pairing of Federer and Wawrinka, who were the gold medal winners at the Olympic Summer Games in Beijing in 2008. Bob Bryan made himself unavailable to play doubles for the U.S. this week after his wife gave birth to their first child last week.
Sunday's reverse singles currently call for the former world No. 1 and currently third-ranked Federer to battle Fish and Wawrinka to encounter Isner.
The 32-time Davis Cup champion Americans are playing here without injured star Andy Roddick.
The U.S. is 2-1 all-time versus Switzerland, including a victory in the final back in 1992. The Swiss, however, are 1-0 all-time against the Americans on home soil, with the victory coming 11 years ago in Basel.
Team USA is captained former world No. 1 star Jim Courier, while Switzerland, which has never captured the Davis Cup, is led by Severin Luthi.
The USA-Switzerland winner will meet the Canada-France victor in the quarterfinals in April.