Joel Eriksson Ek had two goals and an assist, Kevin Fiala had a goal and an assist, and Marc-Andre Fleury made 21 saves for Minnesota (51-21-7), which won its fifth in a row and has points in 10 straight (8-0-2).
The Wild remain tied with the St. Louis Blues for second place in the Central Division with one game in hand. The Blues defeated the Anaheim Ducks 6-3 on Sunday.
The Wild played most of the game without defenseman Jared Spurgeon, who left with an upper-body injury at 12:31 of the first period after taking a hit from Filip Forsberg.
"We just stick together," Minnesota coach Dean Evason said. "It doesn't matter who is in our lineup. We have no complainers. We just go about our business. We were down to five [defensemen]. I think our forwards protected the [defensemen], but I think the [defensemen] did a really good job as well, obviously playing out of position, playing more minutes. It's just a real good all-around game."
Forsberg had a goal and two assists, Mikael Granlund had three assists, and Rittich made 42 saves in his first start since April 10 for Nashville (44-29-6), which was coming off a 6-2 loss at the Tampa Bay Lightning on Saturday.
The Predators are one point ahead of the Dallas Stars for the first wild card into the Stanley Cup Playoffs from the Western Conference.
"Both teams battled hard," Nashville coach John Hynes said. "There was a lot of emotion, a lot of special teams, a lot of momentum swings. But I thought our guys really battled hard tonight. We earned a point. We'd like to get two points, but we've got to take some things out of it and get ready for [the] Calgary [Flames on Tuesday]."