Randy Cunneyworth felt he had a great deal to prove when he was selected in the eighth round, 167th overall, in the 1980 Entry Draft by the Buffalo Sabres. He was convinced he should have been chosen much higher and knew that a successful NHL career would be proper vindication.
As a junior with the Ottawa 67's, Cunneyworth was known for his speed and excellent shot. In his final year of junior, Cunneyworth scored 54 goals and 74 assists for 128 points. He may have carried a small chip on his shoulder as well, having to cool his heels in the penalty box for 240 minutes. When the 67's season ended, Cunneyworth played one game with the Sabres but it was not until the following year that he was able to properly get his feet wet, appearing in 20 games, where he had two goals and six points. For the next three years he patiently played in the minors with the AHL's Rochester Americans.
In 1985-86, he got his first real chance to play in the NHL, when the Pittsburgh Penguins obtained his rights. He played in 75 games for the Pens that year, scoring 15 goals and 45 points. After four years in Pittsburgh, Cunneyworth joined the Winnipeg Jets, but after just 28 games was sent to the Hartford Whalers, where he played the next five years of his career before being traded late in the 1993-94 season to the Chicago Blackhawks.
Cunneyworth joined the Ottawa Senators in the shortened 1994-95 season and remained with the team for another three years. In 1998-99, he signed with the Buffalo Sabres, playing in 14 games before being sent down to the minors with the Rochester Americans. Cunneyworth played 52 games with the Americans in 1999-00 as a player-assistant coach, retiring at the end of the season.
In 2000-01, Cunneyworth took over as head coach of the Rochestr Americans.