The Wild have defeated Nashville in seven of nine meetings.
Minnesota jumped out to a quick 2-0 lead on first-period, power-play goals by Bouchard and Brunette.
With the Wild on a 5-on-3 advantage, Bouchard started the scoring at 6:56. His slap shot from the right faceoff dot beat goalie Dan Ellis high to the glove side.
"When you go into the box as many times as we did against one of the best power plays in the league, you expect to give that team a little life," Ellis said. "With the 5-on-3s, and all the good players on their team, they have a good track record of putting it in the net."
Brunette doubled the lead 35 seconds later with his team-leading fourth power-play goal of the season.
"You start the game, you get the power play, you get two goals, and everyone feels good as long as you keep playing the same way," Minnesota coach Jacques Lemaire said. "We're doing really good things with the puck."
Owen Nolan's power-play tally at 4:09 of the second extended the Wild's lead to 3-0. After going without a goal for eight games, the 36-year-old Nolan has scored in three straight.
Koivu scored the only even-strength goal for Minnesota.
"The key for us was playing as a team for the whole 60 minutes," Koivu said. "We kept it kind of tight and got a big win for us,"
Josh Harding, in his second start of the season, made 25 saves for his first win.
"At the beginning I was a little shaky and obviously nervous," Harding said. "When I am called upon as a backup goalie, it's my job to try to give the team a chance to win, and tonight I think I definitely did that."
Ellis fell to 8-10-2.
Minnesota went 8-5 in November, a franchise record for wins in the month. ... Wild C James Sheppard played in his 100th NHL game. ... Harding's victory was his first since Feb. 10. ... Arnott has four goals in four games.