Stanley was a key member of the 1986 Red Sox team that came within one strike of winning the World Series but ultimately fell to the New York Mets in seven games. Stanley entered Game 6 with the Red Sox one out away from clinching their first World Series since 1918. But his wild pitch to Mookie Wilson allowed the Mets to tie the score, and then New York won Game 6 on Bill Buckner's fielding error that allowed Ray Knight to score from second base. Stanley and the Red Sox would return to Shea Stadium for Game 7, in which the New York Mets would ultimately be victorious by a score of 8–5.