[3] On 7 April 2020, Barabanov having played seven seasons in the KHL with Saint Petersburg, opted to pursue a career in the National Hockey League (NHL) by signing a one-year entry-level contract with the Toronto Maple Leafs.

[4] In the pandemic-delayed 2020–21 season, Barabanov remained on the Maple Leafs opening night roster and made his NHL debut in a 5–4 overtime win over the Montreal Canadiens on 13 January 2021.

[5] Playing in a reduced role, due to the Maple Leafs forward depth, Barabanov appeared sporadically in 13 regular season games collecting one point, a primary assist on a T. J. Brodie goal in a 3–2 victory also over the Canadiens, on 7 April 2021.

[6] In an assignment to the Maple Leafs American Hockey League (AHL) affiliate, the Toronto Marlies, Barabanov showed his offensive acumen in collecting five points through two games.

[11][12] Following four seasons in the NHL, on 1 August 2024, Barabanov opted to return to his homeland to continue his career, signing a two-year contract with Ak Bars Kazan of the KHL.