As a junior, Randy Moller was a standout defenseman with the Lethbridge Broncos of the WHL. He was selected 11th overall by the Quebec Nordiques in the 1981 Entry Draft.
Before he ascended to the NHL ranks, he joined his older brother, Mike, for a World Junior Championship victory against the Czechs in 1982. The elder Moller scored the tournament's winning goal.
The younger Moller then joined the Nordiques for one playoff game at the end of the season. It was just enough to sample the high-pitched rivalry that existed, especially between his team and the Montreal Canadiens. When he returned for full-time duty the following year, he assumed a role as an enforcer whose job was to move the puck and to use his size to good advantage in clearing his defensive zone.
Moller remained an effective member of the Nordiques' blueline for seven seasons. He skated through most of the "Battles of Quebec" with the Stastny brothers, Michel Goulet and Dale Hunter before being dispatched to the Rangers in 1989.
In New York, Moller continued to play his usual physical game until a shoulder injury eliminated any thoughts of being an enforcer. From then on, he reduced his role to that of a defensive defenseman.
After playing parts of three seasons with the Buffalo Sabres, he was traded to the Florida Panthers in 1994. But his ailing knee and back finally gave way, forcing him to retire after only 17 games.