Despite the win, New York is eliminated from post-season play for the first time since 1993.
Mussina (19-9) allowed four hits over five scoreless frames to become the first pitcher in major league history to win 19 games three times without ever winning 20. Mussina will go for his 20th victory in the final game of the season Sunday in Boston. Mariano Rivera pitched a perfect ninth to record his 38th save of the year.
Robinson Cano drove in a run and scored for the Yankees, who have won six straight games. Giambi scored twice.
Jesse Litsch (12-9) took the loss after giving up three runs on five hits over seven innings while striking out eight and walking one.