I've heard that the long running show The Harlem Globe Trotters was based on a real basketball match, that took place in the 40ies I think...
What was that match, and what context made it become a basketball show?
Wikipedia would largely disagree with you:
The Globetrotters originated in the south side of Chicago, Illinois, in the 1920s, where all the original players were raised. The Globetrotters began as the Savoy Big Five, one of the premier attractions of the Savoy Ballroom opened in November 1927, a basketball team of African-American players that played exhibitions before dances. In 1928, several players left the team in a dispute. That autumn, several of the players, led by Tommy Brookins, formed a team called the "Globe Trotters" and toured Southern Illinois that spring.
The article goes on to note that the Globetrotters did win the World Professional Basketball Tournament in 1940; perhaps that is the story which has been confused with what you heard?