Point was a big reason the Tampa Bay Lightning won the second Stanley Cup championship in their history in 2020, defeating the Dallas Stars in a six-game Final. He led all players in the postseason with 14 goals; the last one, a power-play goal at 12:23 of the first period in Game 6, turned out to be the Cup-winner.

The Lightning struck gold when they selected Point in the third round (No. 79) of the 2014 NHL Draft after he scored 91 points (36 goals, 55 assists) in 72 games for Moose Jaw of the Western Hockey League.

On March 26, 2015, Point signed a three-year, entry-level contract with the Lightning and played the final nine games of the American Hockey League season with Syracuse, finishing with four points (two goals, two assists).

After playing the 2015-16 season with Moose Jaw, where he scored 88 points (35 goals, 53 assists) in 48 games, Point made the Lightning out of training camp in the fall of 2016. He made his NHL debut against the Detroit Red Wings on Oct. 13 and scored his first goal in a 4-1 win against the New Jersey Devils on Nov. 5. He finished the season in the top 10 in rookie scoring with 40 points (18 goals, 22 assists) in 68 games.

In 2017-18, Point played all 82 games and was third on the Lightning with 66 points (32 goals, 34 assists). On Jan. 24, he was named to the 2018 NHL All-Star Game as a replacement for injured Lightning defenseman Victor Hedman. Point had 16 points (seven goals, nine assists) in 17 Stanley Cup Playoff games before the Lightning were eliminated by the Washington Capitals.

Point enjoyed a breakout season in 2018-19. He established himself as an offensive force by scoring 41 goals, including 20 on the power play, and finishing with 92 points, third on the Lightning in each category. He was also second at plus-27 and helped the Lightning finish with 62 victories, tying the NHL single-season record for wins set by the 1995-96 Red Wings. He followed that by scoring 25 goals and 64 points in 2019-20, then scored 14 goals and 33 points in 23 games during Tampa Bay's championship run. He led the playoffs in goals for the second straight season to help the Lightning win back to back Stanley Cup championships with 14 goals and 23 points. He signed an eight-year, $76 million contract ($9.5 average annual value) July 28, 2021.

Two seasons later, Point's 51 goals led the Lightning and ranked fifth in the NHL.

Point played his 500th NHL game Oct. 10, 2023, a 5-3 win against the Nashville Predators, to become the 11th skater in Lightning history to reach the milestone. He was named to Canada's roster for the 4 Nations Face-Off during the 2024-25 season, scored his 300th NHL goal in the Lightning's 8-0 win against the Utah Hockey Club on March 27, 2025.

Though Point was named to Team Canada's preliminary roster for the Olympic Winter Games Milano Cortina 2026, he was replaced by Carolina Hurricanes forward Seth Jarvis because of an injury. He returned to the Lightning after the Olympic break and had two assists in his 700th NHL game, a 5-2 win at the Toronto Maple Leafs on March 7, 2026.