Kane's father, Perry, was an amateur boxer, so he named his son after former heavyweight boxing champion Evander Holyfield.

Signed by Vancouver of the Western Hockey League at the age of 15, Kane played just eight regular-season games and seven postseason games as Vancouver won the 2006-07 Memorial Cup. Still rookie-eligible in 2007-08, Kane scored 24 goals in 65 games and was a finalist for the Jim Piggott Memorial Award that goes to the WHL's top rookie.

Finishing with 48 goals, 96 points and a plus-51 rating in 61 games for Vancouver in 2008-09, Kane was named to the WHL Western Conference First All-Star Team and played in the Top Prospects Game in the Canadian Hockey League.

The Atlanta Thrashers selected Kane with the No. 4 pick in the 2009 NHL Draft.

Kane made his NHL debut with the Thrashers and had an assist for his first NHL point on Oct. 3, 2009, against the Tampa Bay Lightning. His first NHL goal came in the next game, Oct. 8, 2009, against the St. Louis Blues, and he finished his rookie season with 14 goals.

He led the Thrashers with 151 hits in 2010-11 and scored 19 goals. The Thrashers relocated to Winnipeg to become the Winnipeg Jets in 2011-12, and Kane responded with a 30-goal season. At the age of 20, he was the NHL's youngest 30-goal scorer that season.

Kane's 147 hits led the Jets in 2012-13, and his 190 shots were second in the NHL. He had an eight-game point streak from Feb. 12-26, 2013.

Kane scored his 100th NHL goal on Nov. 17, 2014, against the Pittsburgh Penguins. On Feb. 11, 2015, Kane was traded by the Jets to the Buffalo Sabres, but a shoulder injury sidelined him for the final 27 games of the 2014-15 season, delaying his Sabres debut.

He had an assist in his first game with the Sabres on Oct. 8, 2015, against the Ottawa Senators. He scored his first goal with Buffalo on Oct. 21, 2015, against the Toronto Maple Leafs and finished the season with 20 goals. Kane's 21:02 of average time on ice was second among Sabres forwards.

Kane had 28 goals and an NHL career-high 113 penalty minutes in 2016-17. He scored 20 goals in 61 games for the Sabres before being traded to the San Jose Sharks on Feb. 26, 2018. Kane had nine goals in 17 games for the Sharks after the trade and signed a seven-year contract with San Jose on May 24, 2018.

In his first full season with the Sharks in 2018-19, Kane matched his NHL career high with 30 goals. His 26 assists and 56 points were one short of his NHL career best in each category.

Kane signed with the Edmonton Oilers as a free agent Jan. 27, 2022 after his contract was terminated by the Sharks on Jan. 9. He did not play for the Sharks in 2020-21 after being suspended by the NHL for 21 games Oct. 18 for violating NHL COVID-19 protocol. He had 39 points (22 goals, 17 assists) in 43 regular-season games for the Oilers and 17 points (13 goals, four assists) in 15 Stanley Cup Playoff games. tying Nathan MacKinnon of the Stanley Cup champion Colorado Avalanche for most goals in the postseason. Kane signed a four-year, $20.5 million contract with the Oilers on July 13, 2022.

Kane had one shot in 14:46 of ice time in his first game since Game 2 of the 2024 Stanley Cup Final, a 6-2 loss to the Los Angeles Kings in Game 2 of the Western Conference First Round on April 23, 2025. He had surgery Sept. 20 to repair two torn hip adductor muscles, two hernias and two torn lower abdominal muscles, then had arthroscopic knee surgery Jan. 9.

Returning for the 2025 playoffs, Kane had 12 points (six goals, six assists) to help Edmonton return to the Final, a six-game loss to the Florida Panthers. He was traded to the Vancouver Canucks by the Oilers on June 25 for a fourth-round pick in the 2025 NHL Draft.

Internationally, Kane was part of the Canadian team that won gold medals at the 2008 Ivan Hlinka Memorial Cup and the 2009 IIHF World Junior Championship.