Connelly began his pro career with the Montreal Royals of the EPHL, playing 64 games, scoring 28 goals and 49 points. Late in 1960-61, he dressed for three games for the Montreal Canadiens.
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 loss to the Detroit Red Wings.
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.
Connelly played a total of 543 games in the NHL with 133 goals and 174 assists for a total of 307 points. In addition, he played 366 games in the WHA with 167 goals and 162 assists for 329 points.
Received these blue ink signed cards TTM.