Internationally, Perunovich has represented the United States at the 2015 Ivan Hlinka Memorial Tournament, where they finished in fifth place, and the 2018 World Junior Ice Hockey Championships, winning a bronze medal.

[8] While playing for the Hibbing High School Bluejackets Bantam A team in 2014, he was drafted by the Cedar Rapids RoughRiders of the United States Hockey League (USHL).

[9] He opted to continue to play for Hibbing High School, where he led the team to a 37–10–5 record and was named a finalist for Bantam Player Of the Year.

[11] Team USA head coach Derek Plante, who had helped Duluth recruit Perunovich, called him a "very crafty, a smart hockey player.

As a sophomore and junior, Perunovich and Jake Jolowsky won the Section 7A doubles title and qualified for the Minnesota high school boys tennis state tournament for a third consecutive season.

[14] After his senior year, Perunovich then played one season with the Cedar Rapids RoughRiders during which he struggled being away from home and recorded the worst plus-minus in the league.

[1] Perunovich played 42 games for the Bulldogs during the 2017–18 season[1] and recorded his first collegiate goal in a 4–3 loss to Michigan Tech on October 7, 2017.

On October 23, 2018, Perunovich was named the NCAA First Star of the Week after he recorded six points in two back-to-back games against the Maine Black Bears.

[38] He was later announced the winner of the 2020 Hobey Baker Award for being the top National Collegiate Athletic Association men's ice hockey player[39] and NCHC Offensive Defenseman of the Year for the third consecutive season.

[37] Following the conclusion of his junior year with the Bulldogs, Perunovich ended his collegiate career by agreeing to a two-year, entry-level contract with his drafting club, the St. Louis Blues, on March 28, 2020.

[41] He was re-assigned to the Blues' American Hockey League (AHL) affiliate, the Utica Comets, to begin the 2020–21 season.

[52] After making the final cut, he scored one goal and two assists during the tournament to help Team USA win a bronze medal.

[53] His only goal of the tournament came during the first outdoor World Juniors game to eliminate a two-goal deficit and beat Team Canada 4–3.