Parise put the Wild ahead to stay with a tally just 24 seconds into the game and turned back a Canucks rally with another goal early in the third period.
Jared Spurgeon notched a goal and an assist while Jason Zucker also tallied for Minnesota, which won for the fifth time in seven games and edged ahead of the slumping Canucks atop the division standings.
Both teams have 28 points, but the Wild own the tiebreaker with two more regulation wins than Vancouver.
Niklas Backstrom earned the victory with 25 saves.
Cory Schneider made 28 saves for the Canucks.