Switzerland and the United States were level at 1-1 in their Davis Cup first round tie after the opening singles on Friday.
Swiss number one Roger Federer's three-set win over American veteran, Todd Martin, got Switzerland off to a flying start.
However, the US team struck back when Jan-Michael Gambill replied with a three-set victory over Switzerland's Michael Kratochvil. Gambill beat the Swiss player in straight sets, 6-4, 7-6 (3), 4-6, 6-1.
Winning the opening set 6-4, Federer needed a tiebreak to clinch the second. Martin then fought back to take the third set 6-4, but the Swiss teenager showed the greater stamina in the fourth to complete a 6-4, 7-6 (7-3), 4-6, 6-1 victory.
"It's for sure one of the top victories I've had so far," said the 19-year-old from Basel, who hammered backhand and forehand passes and, when pressed, stretched for saves and surprised Martin with several deft lobs.
Meanwhile, Gambill picked up his second Davis Cup singles win in five matches. He served 10 aces to four for the Swiss and had only two double faults.
Federer's win and Kratochvil's loss squared Switzerland 1-1 with the United States in the best-of-five encounter.
Switzerland are looking to avenge their defeat at the hands of the United States in the 1992 Davis Cup final, the only previous occasion on which the two sides have met in the competition.
The US team currently in Basel have been weakened by the withdrawals of top stars Andre Agassi and Pete Sampras, although Switzerland are also having to do without Marc Rosset.
swissinfo with agencies