The 25-year-old is the first player in Jets/Atlanta Thrashers history to win the award.
"It's such a great honor," Connor said. "I would love to thank my family and friends. They're always there whenever I need them, and you know, their unwavering support means the world to me."
Connor, who was assessed two minor penalties in 79 games, led Winnipeg and set NHL career highs in goals (47), assists (46) and points (93) this season. He also led Jets forwards in ice time per game (career-high 21:47) and was 12th in the NHL in takeaways (66).
"I think it's being smart with your feet, getting into the right positioning to be able to check with your stick," Connor said. "I just play my game, so in that aspect, is it hard not to take penalties? I don't think about it at all when I'm on the ice. It's just how I've always played the game and always will."
RELATED: [Lady Byng Memorial Trophy winners]
Connor was one of three players to have fewer than 10 penalty minutes while averaging at least 20:00 of ice time per game (minimum 50 games), joining Ryan Pulock of the New York Islanders and Mikey Anderson of the Los Angeles Kings.
"This award, the way I view it, one of my favorite players growing up, being a Detroit kid watching the Red Wings every single night is Pavel Datsyuk. He had a run, winning '06, '07, '08, '09, four in a row Lady Byng trophies," Connor said. "For me, I tried to replicate and do everything he did. I'd watch a ton of YouTube videos. He was so creative and I just loved that. I tried play like Pavel Datsyuk as much as I could. To see it come full circle and get my name as the same trophy as him, it's pretty special."
The award was presented this season by Lucie and Tanya Bossy, the wife and daughter of Mike Bossy, who died following a battle with lung cancer on April 15.
Bossy, one of the greatest goal-scorers in NHL history who helped the New York Islanders win four straight Stanley Cup championships from 1980-83, won the Lady Byng Trophy three times (1983-84, 1986).
"I came across something my father wrote in his book about his first experience winning the Lady Byng Trophy, and I thought I could share that with you," Tanya Bossy said. "He wrote, 'I won my first Lady Byng Trophy as the League's most gentlemanly player. I was happy to get the Lady Byng, but I didn't understand what I did that particular year that I hadn't done in years past.'
"So I think that captures everything about my dad. He was out one way in his everyday life, and one way on the ice, showing sportsmanship and being a gentleman was in his blood. It was just the way he was and the way he acted in his life. He definitely set up a high standard for everyone to look up to for strength, courage and growth, and as a three-time recipient of this award, it is evident that my father considered sportsmanship as being an important part of the game."
Carolina Hurricanes defenseman Jaccob Slavin and Minnesota Wild defenseman Jared Spurgeon were the other finalists. Slavin won the award last season.
