In the 2001 World Series, it was Randy Johnson and Curt Schilling who beat the Yankees. The Yankees went after Javier Vazquez instead of Schilling this winter and could not provide Arizona with young players this summer in order to acquire Johnson's services. While Vazquez had little history against the Yankees, it was he who was the losing pitcher on July 18, 1999 when David Cone pitched his perfect against Montreal.
After the Yankees' offense had been stopped by Arizona in the 2001 Series, Steinbrenner immediately ordered his flunkies to sign free agent Jason Giambi, who was the Oakland Athletics team leader. In the first round of the playoffs, Oakland jumped out to a two game to none lead on the Yankees, but the Yankees won the next three games to eliminate the Athletics.
The Yankees agreed to terms with Giambi on December 13, 2001, which necessitated Tino Martinez' departure. Tino had joined the Yankees, along with Jeff Nelson, on December 7, 1995 after being a part of the Seattle Mariners team that trailed the Yankees in the first round of the playoffs, two games to none, only to sweep the next three to win the series. Martinez and Nelson had beaten the Yankees and then they became Yankees. They were pretty successful.
Alex Rodriguez was once rated by many as the best player in baseball. He was a member of the 1995 Seattle team but had only one plate appearance in the first round of the playoffs against the Yankees. The Seattle shortstop that year was a fellow named Luis Sojo, whom the Yankees acquired in 1996 on waivers and who got an important hit in the 2000 World Series against the Mets.