 The Yankees lost the World Series in 1981 , while the Red Sox loss came in 1986 . Both times , the teams lost after being up 2 – 0 in their respective World Series , and both losses happened in New York ( The Red Sox lost the 1986 World Series at Shea Stadium ) . For the Yankees , the loss in 1981 marked the beginning of the team 's demise and downfall in the 1980s and early 1990s . Despite the lack of championships , the rivalry between the teams did have some memorable highlights . Yankee left @-@ hander Dave Righetti threw a no @-@ hitter against the Red Sox at Yankee Stadium . One of the game 's greatest hitters , Wade Boggs , struck out to end the game . This was the first no @-@ hitter thrown by a left @-@ hander at Yankee Stadium and the first no @-@ hitter by a Yankee since Don Larsen 's perfect game against Subway Series rival Brooklyn Dodgers in Game five of the 1956 World Series and the first regular no @-@ hitter by a Yankee since 1951 . 
