Jackie Robinson breaking the color barrier.
Sorry, we don't allow throughout history questions. These tend to produce threads which are collections of trivia, not the in-depth discussions about a particular topic we're looking for. If you have a specific question about a historical event or period or person, please feel free to re-compose your question and submit it again. Alternatively, you may PM /u/caffarelli to have your question considered for an upcoming Tuesday Trivia thread.
The Miracle On Ice was a huge moral victory for the United States but it didn't really affect policy or anyone outside the USA. The Blood in the Water match between Hungary and the USSR shortly after the Soviets crushed the Hungarian Revolution was an even more politically charged match and seems to be in the theme of what you're asking. http://en.wikipedia.org/w/index.php?title=Blood_in_the_Water_match the Football War between El Salvador and Honduras was sparked by a lot more than an actual game but it seems to have been one more straw on the camels back http://en.wikipedia.org/w/index.php?title=Football_War