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 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.

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. Brandon is the coach of the 2016 Battery Elite team.

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