A defenceman, Finn was drafted 57th overall by the Quebec Nordiques in the 1984 NHL Entry Draft. He played 725 career NHL games, scoring 34 goals and 78 assists for 112 points. During the 1990–91 season he served as Quebec Nordiques team co-captain with Joe Sakic. Finn played most of his career with the Nordiques, but towards the end of his career split parts of three seasons with the Tampa Bay Lightning and Los Angeles Kings.