He would twice lead the Jr. Canadiens in scoring, including the 1963–64 team which featured future Hall of Famers Yvan Cournoyer, Jacques Lemaire and Serge Savard.
When he turned pro in 1964, Boudrias was projected to have a great future for the Canadiens, but his career would stall while former teammates like Cournoyer became stars.
He would see just three games of NHL action over the next three seasons, recording a single assist, while buried in the Canadiens' deep farm system.
However, he would notch 6 points in 14 games in helping the Blues to the Stanley Cup Finals, where they would lose on Bobby Orr's famous goal.
For the 1975–76 season, Boudrias was named the team's captain, but slumped to his lowest totals as a Canuck, finishing with just 7 goals and 38 points as he began to be used in a more exclusively defensive role.
Now in his mid-30s and with his NHL career on the decline, Boudrias left the Canucks following the 1975–76 season to return closer to home, signing with the Quebec Nordiques of the WHA.
He would spend two more successful seasons in Quebec, helping the Nordiques to the WHA Championship with a strong playoff performance in 1977, before retiring in 1978.