1903 Boston Americans
Before there was the Super Bowl, the Stanley Cup, NBA Finals or even the World Cup, there was the World Series. Heck, the World Series predates even the creation of any of the other major sports leagues in America. The National League was long established by the turn of the century as an alternative league was starting up in 1901. There were some finalizing to happen in the next couple season, but by 1903 the "modern era" of baseball had begun.
In this inaugural of baseball as we know it, the Boston Americans were the perfect representatives of the American League. Their name was literally to distinguish themselves from the NL Boston team (the Beaneaters, who would go on to eventually be known as the Atlanta Braves). Player-Manager Jimmy Collins and the Americans coasted to the AL pennant with a 91-47 record, with the 2nd place Philadelphia Athletics 14.5 games back and the last place Washington Senators 47.5 games out.
From the National League, the Pittsburgh Pirates emerged as representatives, with 91 wins of their own. As opposed to how we know it today, the World Series was under a slightly different format in 1903. For starters, it was a best of 9 series, so you need to win 5 games as opposed to 4. The home-away format was different as well, with Boston hosting games 1,2 and 3 in addition to 8 and 9 if necessary while Pittsburgh would host all required games from 4-7.
Game 1 would go the the Pirates 7-3, but Boston would respond with a Bill Dineen Shutout. Pittsburgh would take the next couple games and go up 3-1 in the series. Then the Americans took control, riding the pitching arms of Dineen and Cy Young to flip the script and control the series 4-2 going back to Boston for Game 8. Dineen would pitch another Shutout and Boston would prevail 3-0 to take the first ever World Series.
Young and Dineen combined (because back then "rotations" were for babies and real men pitched until their arm literally fell off) for all of Boston's victories in the series. The team would go on to have more success in the next couple decades with a renaming and the eventual addition of another all time great named Ruth. Unlike other sports leagues to come, the plucky new league didn't roll over for the older guys, helping to quickly legitimize both the American League and the World Series as a whole.