Following high school, Granato was drafted by the New York Rangers in the sixth round, 120th overall, in the 1982 NHL Entry Draft. After a college career at the University of Wisconsin–Madison, Granato made an immediate impact in his first season with the Rangers in 1988–89, leading the team in goals scored (36), which still stands as the team record for goals by a rookie. In what Rangers at the time called "the biggest [deal] in club history", Granato was traded with teammate Tomas Sandström to the Los Angeles Kings on January 20, 1990, in exchange for center Bernie Nicholls.