Alzner was assigned to the Hershey Bears of the American Hockey League to start 2008–09. 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 NHL point on December 4, 2008, against the New York Islanders. 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. Alzner's reactions to this accomplishment were captured in an audio-journal he was keeping for the Hockey Diaries project. Alzner was sent back down to Hershey on January 28, 2009 to make room for returning defenceman Tom Poti. 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. Alzner won his first Calder Cup Championship 2008–09 with the Hershey Bears against Manitoba. In his second season with the Capitals in 2009–10, he was called up to the NHL several times by the Capitals. He played on a defensive pairing with John Carlson in game 7 of the Eastern Conference Quarterfinals vs Montreal. Alzner won his 2nd Calder Cup Championship with the Hershey Bears against the Texas Stars. On July 15, 2011, Alzner signed a two-year contract with the Washington Capitals. On July 10, 2013, Alzner signed a four-year contract extensions with the Capitals. Alzner was then invited by Hockey Canada for the 2014 Olympic orientation camp on July 22, 2013. During the 2015–16 season, on January 27, 2016, Alzner became the Washington Capitals all-time leader in consecutive games played. With 423 consecutive games played he passed Bob Carpenter for the franchise record. The streak began at the beginning of the 2010–11 season.
Montreal Canadiens
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. Alzner cited his frustrations with the Capitals playoff shortcomings and that "he wanted to win" by signing with the Canadiens. However, the Canadiens finished fourth-to-last in the league in Alzner's first season with the club, while the Captials would go on to win the 2018 Stanley Cup. 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. He had played in every NHL game on his team's schedules since 2010. On November 27, 2018, Alzner was put on waivers by the Montreal Canadiens when their star defenceman Shea Weber was activated from the injury reserve. Alzner was not claimed by any other NHL organisation and was assigned to the Laval Rocket of the American Hockey League. On February 22, 2020, Alzner was recalled by the Canadiens, playing in his first NHL game since January 2019.
Personal life
Alzner and his wife Mandy have a daughter and son together.