A native of Anchorage, Alaska, Dubinsky was selected by the New York Rangers in the second round (No. 60) of the 2004 NHL Draft and made his debut against the New York Islanders on March 8, 2007.

He landed a full-time role in the NHL in 2007-08; he scored 40 points (14 goals, 26 assists) in 82 games and helped the Rangers reach the Stanley Cup Playoffs, scoring four goals and four assists in 10 games.

Dubinksy played four more seasons with the Rangers and scored an NHL career high 24 goals in 2010-11. He was traded to the Blue Jackets as part of a package for forward Rick Nash on July 23, 2012.

He scored 50 points (16 goals, 34 assists) for the Blue Jackets 2013-14 and helped them qualify for the playoffs for the second time in their history. Columbus lost a first-round series against the Pittsburgh Penguins, but Dubinsky had six points (one goal, five assists) in six games.

Dubinsky signed a six-year contract with the Blue Jackets on July 11, 2014.

He was limited to 61 regular-season games in 2018-19 and had 14 points (six goals, eight assists), but Dubinsky played in all 10 playoff games for the Blue Jackets, who won a series for the first time with a sweep of the Tampa Bay Lightning.

Dubinsky did not play in 2019-20 because of a wrist injury.