Kucherov also tied for the NHL lead in plus-minus with Montreal Canadiens forward Max Pacioretty at a +38 rating.

[6] On 20 May, Kucherov joined Martin St. Louis as the only players in Lightning history to record two game-winning goals in overtime in a single playoff year, having scored a winner that evening in game three of the Eastern Conference Finals against the Presidents' Trophy-winning New York Rangers on goaltender Henrik Lundqvist; he had scored one in Game 1 of the prior round against the Montreal Canadiens on goaltender Carey Price.

[7] After defeating the Detroit Red Wings, Montreal Canadiens and New York Rangers in the first three rounds, Kucherov and the Triplets would prove to be one of the most dangerous lines in the NHL as Lightning clinched a spot in the 2015 Stanley Cup Finals, in which they would lose to the Chicago Blackhawks in six games.

Kucherov would finish the Lightning's lengthy playoff run with 10 goals and 12 assists for 22 points in all 26 contests played.

He also skated in all 17 Stanley Cup playoff games with the Lightning last season in their run to the Eastern Conference Finals where the Lightning would fall to the Pittsburgh Penguins in seven games, coming just one win short from a second straight appearance in the Stanley Cup Finals, scoring 11 goals, eight assists and 19 points to go along with a +13 rating.

[8] On 29 December, Kucherov recorded his 100th assist on a goal by Ondřej Palát in a 3–2 loss to the Toronto Maple Leafs.

[11][12] On 18 March, Kucherov recorded his 100th career NHL goal in a 5–3 loss to the Washington Capitals on goaltender Braden Holtby.

On 27 March, Kucherov had two assists on goals by Ondřej Palát and Jonathan Drouin in a 5–4 overtime win over the Chicago Blackhawks, setting a Lightning record for most points in a single month with 22.

[16] With his 40th goal, Kucherov joined Steven Stamkos, Vincent Lecavalier, Martin St. Louis, and Brian Bradley as the only players in Lightning history with 40-goal seasons.

[20] On 12 October 2017, Kucherov also became the first player in franchise history to record a goal in five consecutive games to start a season.

In doing so, Kucherov joined Mario Lemieux, Keith Tkachuk, and Steve Yzerman as the only players in the last 30 years to score a goal in each of their first six games.

[23] Kucherov's goal scoring streak was ended the following game on 19 October in a 2–0 win over the Columbus Blue Jackets.

[26] On 10 January 2018, Kucherov was named to the 2018 NHL All-Star Game, which was played at Amalie Arena in Tampa, Florida.

On 15 November, Kucherov recorded his 200th assist on a goal scored by Brayden Point in a 4–3 win over the Pittsburgh Penguins.

[32] On 18 February, Kucherov recorded a five-point night in a 5–1 Lightning win over the Columbus Blue Jackets at Nationwide Arena.

[35] On 14 March, Kucherov recorded his 80th assist of the season on a Brayden Point goal in a 5–4 win over the Detroit Red Wings, becoming the first player since Henrik Sedin in 2009–10 to hit the mark.

[46] On 19 August, Kucherov recorded three assists in a Lightning first-round series-clinching win over the Columbus Blue Jackets on goals by Anthony Cirelli, Kevin Shattenkirk and Brayden Point, respectively.

[48] On 8 September, Kucherov recorded a goal and four assists for a five-point night in an 8–2 Lightning win over the New York Islanders in the first game of the Eastern Conference Final.

[52] Kucherov eventually won the Stanley Cup on 28 September after the Lightning defeated the Dallas Stars in six games.

[59] On 15 June, in game 1 of the 2022 Stanley Cup Finals against the Colorado Avalanche, Kucherov recorded his 100th playoff assist on a goal by Ondřej Palát.

[61] On 13 December 2022, Kucherov recorded his 400th assist on a goal scored by Erik Černák in a 6–2 win over the Seattle Kraken.

On 27 December 2023, Kucherov scored his 300th NHL goal on goaltender Sergei Bobrovsky in a 3–2 loss to the Florida Panthers.

[63] On 18 January 2024, Kucherov recorded his 500th NHL assist on a Steven Stamkos goal in a 7–3 victory over the Minnesota Wild.

[67] On 18 January 2025, Kucherov recorded his 600th career assist on a goal by Darren Raddysh in a 5–1 win over the Detroit Red Wings, becoming the second Lightning player in franchise history to do so.

In 2016 Kucherov made his debut for the Russian national team, joining Lightning teammates Nikita Nesterov, Vladislav Namestnikov, and Andrei Vasilevskiy at the 2016 World Cup of Hockey.