Subban, in his first full season with Montreal, also had an assist in what was the Canadiens' largest offensive output of the campaign.
That assist came on the first goal of the game, which was also the first career NHL goal for Ryan White. He had played in 34 games scattered over two seasons with Montreal.
The Canadiens won for the eighth time in 11 outings. Alex Auld picked up the victory with 30 saves.
Subban's first goal came 51 seconds into the middle period and gave Montreal a 3-0 lead. He added a power-play goal later in the period and then put a slap shot past Niklas Backstrom early in the third.
Backstrom relieved Jose Theodore in the second period after Theodore gave up five goals on 19 shots.
Montreal is in sixth place in the Eastern Conference, two points behind Tampa Bay and five in front of the New York Rangers. With nine games to play, Minnesota is six points out of the final playoff spot in the West.