Paddy Moran started playing hockey at age 15 with Sarsfield, a Quebec City juvenile team. He was educated at St. Patricks School but the school was one of the few local institutions not to have a hockey team in the city. He was 17 when he moved to the Dominions, a junior club, and the team narrowly missed out on the junior title after a one-goal defeat to the Junior Crescents squad. By the age of 19, Moran was tending goal for the Crescent Intermediates and used his stand up style to help the team win an Intermediate Championship.
Moran made his big-league debut with the Quebec Bulldogs of the Eastern Canada Amateur Hockey Association in 1905-06 and stayed with a Quebec-based team for all but one year of his career. He led the National Hockey Association in games won with ten in the 1911-12 season and followed up with a league leading 16 wins in 1912-13. The Bulldogs won the Stanley Cup in both of those seasons and Moran was picked to play for the NHA All-Stars in a 1912 exhibition series.
His Quebec teams, however, tended to lose more games than they won early on and Moran would attempt to keep the puck out of the net in any way possible. Moran played in the days prior to a goal crease being painted in front of the net and guarded his area like a stray dog with a bone. His quick stick was used for more than just deflecting shots and opposition players soon developed a healthy respect for Paddy's self-created "crease." He was a clutch goalie and in the big games was hard to beat.
Moran was particularly proud of the fact that he built his house entirely from his hockey earnings at a cost of about $4,000. He was honoured with induction to the Quebec Hockey Hall of Fame and was a faithful follower of the Quebec Aces Hockey Club in his later years.
Paddy Moran was inducted into the Hockey Hall of Fame in 1958.