Kuzmenko made it to the NHL and North America when he signed a one-year, entry-level contract with the Vancouver Canucks on July 13, 2022. His first NHL season was a rousing success, signing a two-year, $11 million contract Jan. 26, 2023, and scoring 39 goals in 81 games to tie Elias Pettersson for the Canucks lead.

Two seasons later, Kuzmenko was traded to the Calgary Flames by the Canucks on Jan. 31, 2024. He scored 4:20 into his Flames debut, a 4-1 win at the Boston Bruins on Feb. 6. Kuzmenko's goal was the fifth-fastest by a player making his Flames debut ahead of Eddy Beers (1:45) on March 17, 1982. He played two seasons with the Flames before being sent to the Philadelphia Flyers with Jakob Pelletier, a second-round pick in the 2025 NHL Draft and a seventh-round pick in the 2028 NHL Draft, on Jan. 30, 2025, for Morgan Frost and Joel Farabee.

The Flyers traded Kuzmenko to the Los Angeles Kings on March 7, 2025. He signed a one-year, $4.3 million contract with Los Angeles on June 30.

The forward played 11 seasons in his native Russia with his final season his best season in the Kontinental Hockey League. He finished second in the league with 53 points (20 goals, 33 assists) in 45 games for St. Petersburg while leading SKA in points and assists and was second in goals.

Kuzmenko made his KHL debut with CSKA Moscow in 2014-15. He enjoyed a breakthrough season in 2017-18 with 13 goals and 25 points in 45 regular-season games and four goals in 15 games to help CSKA reach the Gagarin Cup finals. He was traded to SKA on Aug. 8, 2018, and in his fourth season had 53 points (20 goals, 33 assists) in 45 games and led SKA with 14 points before a conference final loss to eventual champion CSKA.

Internationally, Kuzmenko helped Russia to a second-place finish at the 2013 World U-17 Hockey Challenge and the 2016 IIHF World Junior Championship, and the Russian Olympic Committee (ROC) to fifth place at the 2021 IIHF World Championship.