Blessed with size and a mean streak to go with a soft touch around the net, Momesso played his junior hockey for the Shawinigan Cataractes of the QMJHL, and was drafted 27th overall in the 1983 NHL Entry Draft by his hometown Montreal Canadiens. He made his NHL debut the following season at the age of just 18, playing a single game for the Canadiens, but remained in junior for most of the following two seasons, during which time he began to dominate the QMJHL and establish himself as a blue-chip NHL prospect. In 1984–85, he recorded 56 goals and 146 points in just 64 games, along with 216 penalty minutes, and was named QMJHL Player of the Year.