Connelly won the Red Tilson Award in 1959–60 as the Ontario Hockey League's most outstanding player while with the Peterborough Petes. Connelly scored 235 points in 4 seasons with the Petes (1956–1960). On November 29, 1961, Connelly scored his first NHL goal in Boston's 7-4 loss to the Chicago Blackhawks. It occurred at Chicago Stadium.
On October 19, 1966, Bobby Orr recorded his first NHL point when he assisted on a powerplay goal by Connelly in Boston's 6–2 win over the Detroit Red Wings. In the NHL's first year of expansion, 1967–68, Connelly led the Minnesota North Stars with 35 goals and 21 assists and received the Hockey News West Player of the Year award. On April 9, 1968, Connelly became the first player to score a goal on a penalty shot in the NHL playoffs when he beat Los Angeles's Terry Sawchuk in a 7–5 victory for his Minnesota North Stars.
He joined the Minnesota Fighting Saints of the upstart World Hockey Association in 1972. He played with the team for four seasons and in 291 games, he scored 144 goals and recorded 283 total points, which were both franchise records. He was traded to the Cleveland Crusaders in the middle of the 1975-76 season before he played sparingly for both the Calgary Cowboys and Edmonton Oilers in the 1976-77 season, after which he retired. In 909 total professional games, he recorded 300 goals with 636 points. He played in 36 WHA playoff games and recorded 16 goals with 15 assists while playing in the Stanley Cup playoffs for 24 games with 11 goals and 7 assists.
Personal life
Connelly and his wife Reg have two children, Ann and Stephen. He lives on Lake Kenogami located near Kirkland Lake in Northern Ontario.