Viktor Arvidsson, James Neal and P.K. Subban also scored for Nashville, which ended a two-game losing streak.
Matt Duchene scored twice and Nathan MacKinnon also scored for Colorado, which has lost six straight.
At the tail end of 2-minute 5-on-3 advantage, Josi took a pass from Ryan Johansen at the top of the left faceoff circle and dropped to one knee as he fired a tiebreaking one-timer by goaltender Semyon Varlamov.
