Lisa Dahlkvist beat US goalkeeper Hope Solo to vault the Swedish side into the Olympic final four for the first time ever on Friday.
The Swedes, who emphasized defence against the star-studded US squad, took a 1-0 lead just past the hour mark on a goal by Stina Blackstenius.
Alex Morgan brought the Americans level in the 77th minute and the teams were knotted 1-1 at the end of regulation, forcing a 30-minute overtime.
Both teams had goals called back late in extra time and the contest went to a penalty shootout, which started badly for the US as Swedish keeper Hedvig Lindahl stopped a less-than-potent shot from Morgan.
The two sides traded successful kicks before Solo made a fine stop on Linda Sembrant to level the tally at 3-3, only for the next U.S. shooter, Christen Press, to send the ball sailing over the crossbar.
Dahlkvist then stepped up, but Solo called a timeout, hoping to spook the Swede.
Though the tactic has worked for Solo in the past, an unperturbed Dahlvist calmly converted to end the US dream of a fourth straight gold medal.