Stillman started his professional career in 1992, when he was drafted sixth overall in the first round by the Calgary Flames. Stillman was tried on both wings, and was quoted saying he liked the left side better but he can play right wing easily if needed. He would play one more season in the OHL with Peterborough, scoring 25 goals and 55 assists in 61 games in 1992-93, upon which he joined the Flames organization with the Saint John Flames of the American Hockey League. Stillman excelled at this level, posting an 83-point campaign (35 goals, 48 assists) across 79 games in the 1993-94. With the NHL in a lockout at the beginning of the 1994-95 season, Stillman remained in the AHL to begin the following season, and in his second season at this level, his performance level improved more, with 28 goals and 53 assists across 63 games.