Forward Zach Parise had three goals and four assists against St. Louis, including two goals in the clinching win.
Minnesota will face the Chicago Blackhawks in a rematch of their 2014 second-round series, which Chicago won 4-2.
The Blackhawks advanced to the second round by eliminating the Nashville Predators with a 4-3, Game 6 victory at United Center on Saturday. They have made it to the second round of the Stanley Cup Playoffs each of the past three seasons and won the Stanley Cup in 2013, when they defeated the Wild in five games in the first round.
The Blackhawks won the first three games against the Wild this season, but Minnesota allowed one goal in winning each of the last two after acquiring goalie Devan Dubnyk in a trade with the Arizona Coyotes on Jan. 16.