Cunneyworth appeared in one game with the AHL affiliate, the Rochester Americans in the 1980–81 season, where he earned an assist. He also was called up to the Sabres from Ottawa on 3-1-81 by Sabres GM Scotty Bowman and played in his first NHL game vs the Boston Bruins in Boston 1980–81, where he was held off the scoresheet. Re-joined the Sabres for the post-season along with other prospects following the end of the OHA playoffs, but did not play in any games. Suffered a serious eye injury (a Barry Melrose high stick) during a September 1981 preseason game at Toronto and missed the remainder of the preseason. Cunneyworth began the season with Buffalo. During the 1981–82 season, he appeared in 20 games, scoring two goals and six points. Played primarily on the CPR (Canadian Pacific Railroad) line with young teammates Steve Patrick and Lindy Ruff. This nickname was given to the trio by then Sabres Assistant Coach Nick Polano. Earned his first NHL assist 10-7-81 against the Washington Capitals. Scored his first NHL goal against the Rangers at Madison Square Garden on 11-11-81 in New York against goalie Steve Weeks. Was reassigned to the Sabres affiliate in Rochester in late November. He spent the rest of the 1981–82 season with the Rochester Americans, playing in 57 games, scoring 12 goals and 27 points. Spent the playoffs with Rochester, scoring four goals in nine games, as the Americans lost to the Binghamton Whalers in the South Division finals. Cunneyworth spent the entire 1982–83 season with the Mike Keenan coached Rochester Americans. Appeared in 78 games scoring 23 goals and 56 points. In 16 playoff games, Cunneyworth had four goals and eight points, helping the Americans win the 1983 Calder Cup Championship defeating the Maine Mariners. Cunneyworth spent another full season in the American Hockey League in the 1983–84 season with Rochester, as he scored 18 goals and 35 points in 65 games, once again helping the Americans reach the playoffs. In 17 post-season games, Cunneyworth scored five goals and 10 points, as Rochester lost to the Maine Mariners in the 1984 Calder Cup finals. During the 1984-85 Buffalo Sabres pre-season, Cunneyworth scored 3 goals and had an assist in 4 exhibition games. He was also among the leading scorers in inter-squad scrimmages but failed to secure a roster spot. The 1984–85 season would be Cunneyworth's third full season with the