On November 2, early in the next season, Graves was involved in a blockbuster trade with the Edmonton Oilers. Along with Graves, the Oilers received Petr Klima, Joe Murphy and Jeff Sharples in exchange for Jimmy Carson, Kevin McClelland and Edmonton's fifth-round draft pick in the 1991 NHL Entry Draft. The trade was lamented at the time in Edmonton—the high-scoring Klima had run-ins with the law and a history of substance abuse, Sharples was coming off a shoulder injury, and Murphy and Graves were considered to be underachievers given their high draft status. Red Wings general manager Jim Devellano was reluctant to part with Graves, but felt that obtaining Detroit-area native Carson was worth it. The trade paid immediate dividends for the Oilers, as Klima finished with 30 goals, while Graves and Murphy provided depth. Graves would go on to score 11 points in the playoffs, en route to defeating the Boston Bruins for the Edmonton Oilers' fifth Stanley Cup.