During the 1993–94 season, Graves scored 52 goals, setting a New York Rangers' franchise record for most goals in a season. (Jaromír Jágr would later score 54 in 2005–06). In the spring of 1994, Graves helped the Rangers win their first Stanley Cup since the 1939–40 season. Graves was awarded a roster spot on the NHL's second All-Star Team at the position of left wing, and was the recipient of the King Clancy Memorial Trophy in recognition of his continuing work with charitable causes. Graves is one of the seven alumni of the Oilers dynasty to win the Stanley Cup with the 1993–94 New York Rangers, along with Jeff Beukeboom, Glenn Anderson, Kevin Lowe, Craig MacTavish, Mark Messier and Esa Tikkanen.