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, holding a one-run lead with runners on first and third. Stanley threw a wild pitch to Mookie Wilson which allowed Kevin Mitchell to score the tying run and Ray Knight to move to second base, putting him in position to score the tying run on Bill Buckner's fielding error. Stanley and the Red Sox returned to Shea Stadium for Game 7, which the New York Mets won by a score of 8–5.