Darrin, who is the younger of the two Shannon brothers (Darryl is two a year older), was a highly touted junior playing out of the OHL's Windsor Spitfires where he scored 83 points in 60 games his first year, 74 in 43 games his second, and 81 points in 54 games his final year. In the talent-rich pool of 1988, Shannon was selected fourth overall by the Pittsburgh Penguins. But, before he could play a game for the Pens, he was traded to the Buffalo Sabres.
Shannon's first taste of the NHL came in a brief five-game stint (including two in the playoffs), with the Sabres in the 1988-89 season. He spent the majority of the next two years in the AHL with the Rochester Americans amassing 103 points in 99 games. Shannon played one game with the Sabres in 1991-92 before being traded to the Winnipeg Jets. The next season saw him finish with an NHL career high in assists with 40 and points with 60.
His brother, Darryl, joined Darrin on the Jets for the 1993-94 season and played together for the next two seasons. When the Jets relocated to Phoenix and changed their name to the Coyotes, Shannon went along. Darrin spent the next two seasons in both the IHL and AHL before retiring from the game in 1999-2000.