Montour's NHL career reached new heights after he was traded to the Florida Panthers by the Buffalo Sabres on April 10, 2021, for a third-round pick in the 2021 NHL Draft. He had 37 points and an NHL-best 73 his first two seasons with the Panthers, respectively, and finished the 2023 Eastern Conference First Round with five goals, the most by a defenseman in a single series since Ed Jovanovski for the Vancouver Canucks in the 2003 Western Conference Semifinals. He opened the scoring in Game 7 and tied it with one minute left in the third period to help the Panthers defeat the Boston Bruins 4-3 in overtime.

Montour scored eight goals in the 2023 Stanley Cup Playoffs to lead defensemen. He became the ninth at the position to score at least that many in a single playoff year, with Brian Leetch (11 for the New York Rangers in 1994), Victor Hedman (10 for the Tampa Bay Lightning in 2020) and Cale Makar (eight for the Colorado Avalanche in 2022) the only ones with as many since the beginning of the 1990s. He became the second Stanley Cup winner of Indigenous descent in as many years, following Zach Whitecloud for the 2022-23 Vegas Golden Knights, when he helped the Panthers defeat the Edmonton Oilers 2-1 in Game 7 of the 2024 Stanley Cup Final.

That earned him a seven-year, $50 million contract (average annual value of $7.14 million) he signed with the Seattle Kraken on July 1, 2024. Montour's goal four seconds into overtime to give the Kraken a 5-4 win against the Montreal Canadiens at Climate Pledge Arena on March 12, 2025, matched the NHL record for the fastest goal to start any period, previously accomplished by Montreal's Claude Provost (Nov. 9, 1957), Denis Savard of the Chicago Blackhawks (Jan. 12, 1986) and James van Riemsdyk of the Toronto Maple Leafs (March 28, 2014).

The Anaheim Ducks selected Montour, an offensive-minded defenseman, in the second round (No. 55) of the 2014 NHL Draft after he had 62 points (14 goals, 48 assists) in 60 games with Waterloo of the United States Hockey League.

Montour played for Waterloo and the University of Massachusetts Amherst in 2014-15 before signing a three-year, entry-level contract with the Ducks on March 16, 2015.

Montour played the following season with San Diego of the American Hockey League and had 57 points (12 goals, 45 assists) in 68 games to be named to the AHL First All-Star Team and All-Rookie Team.

After playing the first half of the 2016-17 season in San Diego, Montour was called up and made his NHL debut in a 3-1 win against the Calgary Flames on Dec. 29, 2016. He scored his first NHL goal in a 3-2 shootout loss at the Tampa Bay Lightning on Feb. 4, 2017, and finished the season with six points (two goals, four assists) in 27 games.

During the playoffs, Montour had seven assists in 17 games to help Anaheim advance to the Western Conference Final.

In his first full season with the Ducks in 2017-18, Montour tied for second among defensemen with 32 points (nine goals, 23 assists) in 80 games and also had a plus-16 rating. During his third season with Anaheim, Montour was traded to the Sabres for defenseman Brendan Guhle and a first-round pick in 2019 NHL Draft on Feb. 24, 2019. He had 18 points (five goals, 13 assists) and led Sabres defensemen with a plus-13 rating in 54 games before the 2019-20 NHL season was paused March 12 due to concerns surrounding the coronavirus.