Americans playing in 72 games for Rochester, scoring 30 goals and 68 points to finish third in team scoring. In five playoff games, Cunneyworth had two goals and three points, as the Americans fell to the Baltimore Skipjacks in the first round of the playoffs. Cunneyworth and teammate Ted Nolan began using local Rochester businessman Steve Bartlett as their representative/agent. Although offered a contract, Cunneyworth elected not to re-sign with the Buffalo Sabres organization, although the team held his rights. Cunneyworth was granted the permission by Sabres GM Scotty Bowman to attend the NHL's Pittsburgh Penguins training camp/preseason roster. On October 4, 1985, following the pre-season tryout, Bowman traded Cunneyworth and Mike Moller to the Pittsburgh Penguins for Pat Hughes. Pittsburgh Penguins (1985–1989) Randy Cunneyworth returned to the NHL for the 1985–86 as a full-time player with the Pittsburgh Penguins. In 75 games, Cunneyworth scored 15 goals and 45 points to finish sixth in team scoring, as Pittsburgh missed the playoffs by two points, finishing in fifth place in the Patrick Division. Was classified as an NHL rookie. In 1986–87, Cunneyworth improved his offensive numbers, scoring 26 goals and 53 points in 79 games to finish third in team scoring behind Mario Lemieux and Dan Quinn, however, the Penguins failed to qualify for the playoffs again, finishing in fifth place, four points out of the post-season. Cunneyworth scored a hat trick in the season opener October 9, 1986 vs Washington, and had a four-goal game @ Quebec March 3, 1987. Recorded 11 multiple point games. Was the Penguins nominee for the Masterton Trophy. The 1987–88 season would be the best offensive season of Cunneyworth's career, as he scored 35 goals and 74 points in 71 games, finishing an impressive third in scoring behind Lemieux and Quinn, however, the Penguins once again failed to qualify for the playoffs, finishing in last place in the Patrick Division despite a 36–35–9 record. Although a consideration, Cunneyworth was not selected by Wales Conference Coach Mike Keenan for the NHL All-Star Game although his point totals ranked among the league leaders for his position at mid-season. Cunneyworth missed 8 regular season games from Jan 16-30 due to an NHL suspension (5 games for a stick incident vs Boston on Dec 29, and 3 games for a match penalty during a fight with Steve Konroyd vs the NY Islanders on Jan 12.) Recorded 20 multiple point