Stevens was taken fifth overall in the 1982 NHL Entry Draft by the Washington Capitals. Due to injuries to other players during training camp, Stevens made the team at age 18 and never played a game in the minor leagues. He made an immediate impact, scoring on his first shot in his first NHL game. He scored 25 points in his debut season and made the All-Rookie Team. In addition, he led all rookie defencemen in penalty minutes. He finished third in the voting for the Calder Memorial Trophy, which is awarded to the league's Rookie of the Year. He was also named the Capitals' Rookie of the Year. Stevens' debut with the Capitals coincided with the team's first playoff appearance, although they were eliminated in the first round by the New York Islanders.