In an era when American professionals could not participate in the Olympics, the US team of mostly college players had rallied in 1972 to lead 50-49 as time ran out.
But an international basketball official, William Jones of Britain, ordered the game clock reset to three seconds, and on a second replay of the final ticks of the clock the Soviets scored a layup and were awarded the gold medal.
"(Jones) overruled the referee and the official scorer," Kenny Davis, the US team captain, said. "He has absolutely no power at all to do that."
The incredulous Americans voted not to accept silver medals.
Davis and a team-mate remain so angry that they put in their wills that no one in their families can accept the medal either.
Soviet players and coaches have called the final result legitimate, saying the buzzer system to call timeouts had malfunctioned, and that the Americans were being sore losers.
"Americans, out of their own national pride and love of country, they didn't want to lose, especially in basketball," a sport invented in the United States, Russian player Ivan Edeshko said in an ESPN documentary.
The Soviets' 51-50 triumph ended the United States' 63-game unbeaten streak in the Olympics and its string of seven consecutive gold medals since the sport was introduced in 1936.
Four decades after the defeat, the American players will reunite next month at Davis' alma mater, Georgetown College in central Kentucky, for the first time since that Olympics. There will be a dinner and seminars open to the public.
While the defeat left US players bitter, it has since been seen as a watershed moment that inspired players all over the world. At the time, there were no foreign players in the National Basketball Association. Non-Americans now make up more than one-quarter of the rosters.
The United States reasserted its dominance in international basketball with its first "Dream Team" in 1992 after professionals were allowed to compete, a team which featured Michael Jordan, Magic Johnson and Larry Bird.
The Soviets again won gold at the 1988 Games, and Argentina triumphed in 2004 even after professionals were allowed.
In the 2008 Olympics, the US squad won gold, and the 2012 team in London will be stocked with a dozen stars selected from among 17 players led by NBA stars LeBron James and Kobe Bryant.
The 1972 American basketball defeat took place in a funereal atmosphere after one of the most notorious events in Olympic history in Munich - the massacre of 11 members of the Israeli team by Palestinian commandos.
The 1972 game ended in chaos. With the United States ahead 50-49, the Soviets inbounded and time ran out. But a referee blew his whistle because a Soviet assistant coach was gesturing frantically that they had tried to call a time out.
Then Jones interceded, ordering the game clock reset to three seconds.
The final three seconds were replayed twice because the clock was not properly reset the first time. After the first Soviet miss, the Americans thought they had won and in the bedlam that followed one US player nearly had his jersey ripped off, and US coach Hank Iba's wallet was pickpocketed.
Finally, Soviet center Aleksandr Belov gathered in a court-length pass, shed two US defenders, and shot a lay-up for the win.
"If you ask any of the 12 US players, they will tell you the same thing: They would have replayed that last three seconds as many times as was needed for the Russians to win that game," said Don "Taps" Gallagher, a Chicago lawyer and author of "Stolen Glory," a book coming out this month on the controversy.
Belov died in 1978, and was buried with his gold medal.
The player guarding Belov at the end, Jim Forbes, now a high school teacher and coach, told Gallagher he thinks about the defeat every day, believing he let his country down.
Tom McMillen, who became a US congressman, and Gallagher sought to rectify the 1972 result, asking the International Olympic Committee for reconsideration and noting there is a precedent for declaring a co-winner. A French skating judge admitted to bias at the 2002 Salt Lake City Winter Games, and a second set of gold medals were awarded.
Davis, for one, does not like the idea. "In a basketball game, there is a winner and a loser. There's no such thing as a co-winner," he said.
"Anybody who saw the last few minutes and knows the rules knows that we got cheated," said Ed Ratleff, a star guard who subsequently played professionally in the NBA, coached, and is now an insurance executive.