October 8th 1956:

Don Larsen of the New York Yankees pitches the first and only perfect game in World Series History. The Yankees beat the Brooklyn Dodgers 2-0 and the opposing pitcher, Sal Maglie, only gave up 5 hits in the loss.

 

October 8th 1986:

Mike Scott of the Houston Astros ties a playoff record with 14 strikeouts in a 1-0 win over the Mets in the first game of the NLCS. The Mets, of course, went on to win the NLCS and eventually the World Series.