He was originally selected by Salavat Yulaev Ufa in the first round, seventh overall, of the 2011 KHL Junior Draft.

[5] Vasilevskiy had compiled a record of 8–3–3 in 14 appearances with Syracuse that season, with a 2.34 GAA, .918 save percentage and two shutouts.

On 3 September, Vasilevskiy had successful surgery to remove a blood clot from near his left collarbone and to treat a type of thoracic outlet syndrome.

On 1 November, the Lightning recalled Vasilevskiy from his conditioning stint with the Crunch, where he made 56 of 58 saves in two wins.

Despite Vasilevskiy's strong performance, the Lightning lost in seven games, one win shy of a second consecutive appearance in the Stanley Cup Finals.

[15] On 28 December, Vasilevskiy recorded his first career NHL point as an assist on an overtime goal scored by Tyler Johnson, which came in a 4–3 victory over the Montreal Canadiens.

On 26 October 2017, Vasilevskiy played in his 100th career NHL game in a 3–2 win over the Detroit Red Wings.

[20] This also made Vasilevskiy only the sixth goalie in NHL history to record 20 wins in 25 games played.

[36] Vasilevskiy returned 4 weeks later, starting his first game back on 13 December, at home against the Toronto Maple Leafs.

That night his 48 saves tied Ben Bishop's team record from four seasons prior, as the Lightning defeated the Leafs 4–1.

[37] On 8 January 2019, Vasilevskiy was added to the Atlantic Division roster for the 2019 National Hockey League All-Star Game as a replacement for an injured Carey Price.

[38] On 15 January, Vasilevskiy recorded a shutout in a 2–0 Lightning win over the Dallas Stars at American Airlines Center.

[43] In a 13-save victory over the Boston Bruins on 25 March, Vasilevskiy moved past Ben Bishop for the most saves in franchise history, with 5739.

Vasilevskiy was named a finalist for the Vezina Trophy for the third consecutive season (which eventually was awarded to Connor Hellebuyck of the Winnipeg Jets).

[49] On 25 August, Vasilevskiy recorded an overtime victory over the Boston Bruins in the second game of their second round series.

On 7 July 2021, Vasilevskiy posted a 1–0 shutout against the Montreal Canadiens to take win the series 4–1, as the Lightning clinched their second consecutive Stanley Cup.

On 23 May 2022, Vasilevskiy posted his NHL record-breaking sixth series clinching shutout with a 49 save shutout against the Presidents' Trophy-winning Florida Panthers in a four game sweep, finishing the series with an astonishing .981 save percentage, as he allowed only three goals out of 154 shots.

[62] In winning the 2014 IIHF World Championship with the Russian senior team, Vasilevskiy was awarded the Order of Honour on 27 May 2014.

[66] His father, Andrei Vasilevski (born 1966), was also a goaltender who competed in the Russian Superleague as a member of Salavat Yulaev Ufa.