First fanpost, feel free to edit. Comment, please! There's a lot to write, so add as much as you want in the comments.
It was the 2002 FIBA World Cup, played in US territory, the city of Indianapolis. For the first time in history, a USA team full of NBA players was defeated, since the Dream Team of '92 made it's first appearance. It was the 4th of September of 2002 when Argentina beat USA 87-80 for the last match to play in Group F.
Manu Ginóbili made 15 points, 3 assists and 2 steals; Fabricio Oberto made 11 points, 9 rebounds, 2 assists. It was a classical Argentina team, with some guys that played later in the NBA, like Ginóbili, Oberto, Nocioni and Scola; and the two first Argentines to play in NBA, point-guard Pepe Sánchez and center Rubén Wolkowisky. It had some other great basketball players, like Alejandro Montecchia, Hugo Sconochini, Leandro Palladino (a favorite of mine) and actual member of Argentina team Leonardo Gutiérrez.
Some of the names that played for USA were Paul Pierce, Michael Finley, Reggie Miller, Andre Miller, Shawn Marion, Jermaine O'Neal, Ben Wallace and Elton Brand. Pierce made 22 points, Finley and A. Miller scored 14 each.
The day after this game, USA lost with Yugoslavia (81-78) in Quarter-Finals, which would win the tournament in a polemic final against Argentina in OT 84-77. USA would finish 6th, the worst position in this kind of competition in a thousand years or something like that (I made it up, but it's probably correct). It was the last time Yugoslavia would play in a world competition, but Argentina took some revenge when they beat Serbia & Montenegro in 2004 Olympics with a buzzer-beater of our own Manu, and finally winning the Olympic Gold.
PS: If you're in Argentina, there's a TV special in ESPN+ at 23:00 local time.