Brek Shea rifled home a free kick at the end of the first half to give Juergen Klinsmann's team a deserved lead but they were pegged back by with 10 minutes left after poor defending.
The visitors, who have won only two out of nine games since the World Cup as they undergo a rebuilding process, played the last quarter of the match with 10 men after having Jozy Altidore sent off.
Altidore, one of the most experienced players on the U.S. team, clipped an opponent from behind and was sent off as he argued about the decision with referee Luca Banti.
The U.S. conceded two goals in the last 10 minutes in last week's 3-2 defeat to Denmark and also gave away late goals in friendlies against Honduras (1-1), Ecuador (1-1), Colombia (1-2) and Ireland (1-4).
Nevertheless, Klinsmann was encouraged. "We are getting close to the 90 minutes we were playing at the World Cup," he told reporters.
"Overall, I saw a lot of good stuff from the entire group; it was enjoyable to see that everyone was throwing themselves in there to get a result against a good team...
"I told the players at halftime, you can commit fouls but never joke with an Italian referee," he added.
Shea broke through when he fired his effort over the wall and into the net, helped by poor positioning from Switzerland keeper Roman Buerki, with the last kick of the first half.
Minutes earlier, Admir Mehmedi missed an open goal for the Swiss, failing to make contact with the ball when Xherdan Shaqiri's low cross found him free in front of goal.
Switzerland turned the screw in the second half and had already threatened several times before Stocker scored from close range after the U.S. failed to deal with a cross whipped in from the left.
(Editing by Toby Davis)
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