Svechnikov made his NHL debut on 4 October 2018, going scoreless in a 2–1 loss to the New York Islanders.[10] One day later, he recorded his first career NHL point (an assist) in a 3–1 win over the Columbus Blue Jackets.[11] On 7 October, Svechnikov scored his first career NHL goal during an 8–5 win against the New York Rangers. In doing so, he became the first player born in the 2000s to score an NHL goal.[12] Svechnikov finished his rookie season with 20 goals and 17 assists for 37 points. He also recorded 5 points in 9 postseason games.
On 29 October 2019, Svechnikov become the first NHL player to score a Michigan goal, doing so against David Rittich in a 2–1 win over the Calgary Flames.[13] He scored a similar goal on 17 December against the Winnipeg Jets.[14] He greatly improved on his previous season, scoring 24 goals and 37 assists for 61 points. The Hurricanes matched up with the Rangers in the 2020 Qualifying Round.[15] In Game 2 of the series, Svechnikov scored a hat-trick during a 4–1 win. The feat was the first in Hurricanes/Hartford Whalers franchise postseason history.[16]
On 26 August 2021, Svechnikov agreed to an eight-year, $62 million contract with the Hurricanes.[17] On 11 March 2023, Svechnikov's 2022–23 season ended when he suffered a season-ending knee injury during a 4–0 loss to the Vegas Golden Knights. He appeared in 64 games, recording 23 goals and 32 assists for 55 points during the season.[18]
Svechnikov's father, Igor, worked as a pediatrician on Sakhalin Island, but after the 1995 Neftegorsk earthquake gave up the practice and moved his family to Barnaul in Siberia, and sold cakes in the region. Svechnikov's mother, Elena, worked two jobs: reception at a hockey rink during the day, and cleaning floors at night. With Elena's connection to the hockey rink both of her sons took an early interest in hockey, and Svechnikov began skating when he was 3.[1]
In order to help both of their sons develop in hockey, Igor and Elena moved to Moscow, though after one year they were recruited by Ak Bars Kazan, so the family moved to Kazan.[1][19] When Svechnikov moved to Michigan to play in the USHL, Elena joined him, and with Evgeny playing nearby they would all frequently spend time together.[1]