[2] Alzner played four Western Hockey League (WHL) seasons with the Calgary Hitmen as part of a standout junior career.

He was called up to the Washington Capitals roster on November 26, 2008, making his NHL debut that night against the Atlanta Thrashers.

He recorded his first goal the next game on December 6, 2008, on Hockey Night in Canada against Vesa Toskala of the Toronto Maple Leafs.

He was recalled during the Capitals' playoff series with the Pittsburgh Penguins on May 3 as a precautionary measure after injuries to several Washington defencemen, but did not see any action.

[8] On July 1, 2017, having left the Capitals as a free agent after nine seasons, Alzner agreed to a five-year, $23.125 million contract with the Montreal Canadiens.

However, in an ironic twist of fate, the Canadiens as a team finished fourth-to-last in the league in Alzner's first season with the club, 26 points out of a playoff spot while the Capitals would finish the 2017–18 season as the second seed in the Eastern Conference and fifth in the league overall and then go on to win the Stanley Cup for the first time in franchise history having defeated the Vegas Golden Knights in five games in the 2018 Stanley Cup Finals.

On October 3, 2018, with the Canadiens' set to open the 2018–19 season against the rival Toronto Maple Leafs, Alzner was announced as a healthy scratch.

With the decision, Alzner's iron man streak, the fourth longest among active players at the time, ended.

On November 27, Alzner was put on waivers by the Montreal Canadiens when their star defenceman and captain Shea Weber was activated from the injury reserve.