Minnesota won its 21st home game of the season and only Anaheim has more in the Western Conference.
The Wild twice took a one-goal lead, but on both occasions Craig Smith tied it up.
Jonas Brodin opened the scoring 4:05 into the game and Smith created a 1-1 tie just 1:45 later.
Zach Parise, who will captain the U.S. Olympic team at the Winter Games in Sochi, Russia, again boosted the Wild in front late in the opening period only to have Smith score the only goal of the second period.
Darcy Kuemper had to make just 16 saves to get the win. Nashville lost its second in a row, getting 33 stops from Carter Hutton.