In his first season in the Ontario Hockey League (2013-14), Dunn had 33 (five goals, 28 assists) points in 63 games with Niagara to finish second among defenseman in scoring. He increased his offensive output to 56 points (18 goals, 38 assists) in 68 games the following season and was named to the Canadian Hockey League's Top Prospects Game before he was selected by the St. Louis Blues in the second round (No. 56) of the 2015 NHL Draft.

Dunn signed a three-year, entry-level contract with the Blues on Sept. 24, 2015. In 2015-16, he had 43 points (12 goals, 31 assists) in 52 games with Niagara. The following season, Dunn had 45 points (13 goas, 32 assists) in 72 games with Chicago of the American Hockey League, leading the team among defensemen.

Dunn made the opening night roster for the Blues in 2017-18, making his NHL debut in a 5-4 overtime win against the Pittsburgh Penguins on Oct. 4. He scored his first NHL goal in a 5-2 loss to the Florida Panthers on Oct. 12 and finished the season with 24 points (five goals, 19 assists) in 75 games, which led all Blues' rookies. He was even better in 2018-19, finishing with 35 points (12 goals, 23 assists) in 78 games, then contributing eight points (two goals, six assists) in the playoffs to help the Blues win their first Stanley Cup championship.