Graves played two seasons for the Oilers before becoming a free agent at the end of the 1990–91 campaign. He then signed an offer sheet for five years and $2.44 million with the New York Rangers, where he was soon joined by other former Edmonton Oilers teammates Mark Messier and Jeff Beukeboom. Neil Smith, the general manager of the Rangers, was familiar with Graves, having earlier served as the Red Wings' director of scouting. In Graves' first season with the Rangers, he scored 26 goals, helping the team to a 105-point, Presidents' Trophy-winning season. Graves finished fifth in the voting for the Frank J. Selke Trophy for best defensive forward.