Final answer:
Professional baseball was the first sport to successfully employ the league structure, with the formation of the National League in 1876 after the Cincinnati Red Stockings became the first salaried team in 1869.
Step-by-step explanation:
The first sport to successfully employ the league structure was professional baseball. The Cincinnati Red Stockings became the first salaried team in 1869, setting the stage for the growth of professional baseball leagues. By 1876, the National League was formed, establishing a more formalized league structure that would become integral to the development of professional sports leagues.
With the establishment of the National League and other leagues that followed, the foundation for modern sports leagues was created. This would later be mirrored in various sports, including the Negro National League, formed in 1920, which was the first commercially successful African American baseball league, highlighting the importance and success of the league structure in sports.