At the conclusion of the season, Point was selected in the fifth round, 167th overall by Traktor Chelyabinsk in the 2013 KHL Junior Draft.

[4] At the conclusion of the season, Point joined the Lightning's American Hockey League (AHL) affiliate, the Syracuse Crunch.

On October 11, 2016, the Tampa Bay Lightning announced that Point had made the opening night roster out of training camp.

Lightning centre and captain Steven Stamkos stated that he believed Point deserved to play in the NHL.

[citation needed] Lightning general manager Steve Yzerman stated that the team "felt like he's earned the right for us to give him a look right off the bat.

"[5] On October 13, Point made his NHL debut in a 6–4 Lightning win over the visiting Detroit Red Wings.

[7] On October 18, Point recorded his first NHL shootout goal on his first attempt against goaltender James Reimer of the Florida Panthers.

The goal came on the power play off a redirection of a Nikita Kucherov slap shot, which beat Devils' goaltender Cory Schneider.

[16][17] On April 14, Point recorded his first career playoff goal, which came in game two of the series, ending in a 5–3 Lightning win over the Devils at Amalie Arena.

[24] On September 7, Point recorded a five-point night to help the Lightning to a 8–2 win over the New York Islanders in the first game of the Eastern Conference final.

[31] Brayden was also named to the Team Canada roster that captured a gold medal at the 2015 IIHF U20 World Junior Championships.

[32] On April 12, 2017, Point was named to Canada's men's national ice hockey team for the 2017 IIHF World Championship.