In Connor's last year of junior hockey, he was named captain of the Flin Flon Bombers in the WCHL and scored 44 goals, 41 assists in 91 games, along with a staggering 376 penalty minutes.. Connor won the Rookie of the Year award. He claims a lot of this success is due to his coach Pat Ginnell having the confidence in him to make him captain. Because of Connor's junior success, he was selected by the Montreal Canadiens in the first round, fifth overall in the 1974 NHL amateur draft. Connor was also selected by the Phoenix Roadrunners in the first round, fourth overall in the 1974 WHA Secret Amateur Draft. The Roadrunners offered Connor a lot of money, and he ended up choosing the WHA instead of the Canadiens, a move he says he now regrets. Montreal coach Scotty Bowman offered to beat the WHA's offer, but Connor had already given his word and did not want to go back on it. Connor began his World Hockey Association career with the Phoenix Roadrunners before a stint with the Houston Aeros where he played with Gordie Howe and his sons Marty and Mark Howe. He found great success in the WHA and was selected to the 1977 All Star Team. When the Houston Aeros folded he joined the Montreal Canadiens in 1978. Coached by Scotty Bowman, during the Habs dynasty years, Montreal's was a tough line-up to crack, but Connor did suit up for 23 games that season. He is remembered for his series-winning double OT playoff goal against the Toronto Maple Leafs. During his time with the Habs, Connor was plagued with injuries and severe food poisoning, and league rules said Connor did not play enough playoff games to have his name engraved on the Cup. His teammates rallied around him and said if his name was not on the Cup, none of their names should be on the Cup. The league reversed their decision and his name was included on the Stanley Cup. For the Edmonton Oilers' first year in the NHL, they selected Connor as the number one pick in the expansion draft. He played with a rookie Wayne Gretzky, making him one of two players to play with both Gretzky and Gordie Howe. Connor was coached by Glen Sather, and was traded to the New York Rangers after one season, learning about his trade over the radio. Connor battled chronic injuries during his three seasons with the Rangers. He performed well in the playoffs and scored 4 goals in 4 games. He broke his back in two spots and ended his career Tulsa Oilers.
After hockey
He became the assistant coach of the American Hockey League's New Haven Nighthawks following his playing career. For the first Heritage Classic, Connor was selected to the Montreal Canadiens legends team. He was one of two players present to have played on both the Oilers and Canadiens. Connor was inducted into the Manitoba Hockey Hall of Fame in 2016. Connor has been seen at charity events, motivational speaking and hosts a podcast, "View from the Penalty Box". He competed on the All Athletes All Star edition of Wipeout Canada on April 24, 2011.
