Niederreiter scored his second at 7:08 of the second period for a 2-1 lead, and Joel Eriksson Ek made it 3-1 at 17:32 with his third NHL goal.
"I think our first period was good," Ottawa coach Guy Boucher said. "I think the minute they got that second goal there, we didn't look good after. … I know we [have] injuries, but the guys that were in the lineup are able to play better than that."
Matt Dumba scored a power-play goal at 4:46 of the third period to increase the Wild lead to 4-1, and Jason Pominville made it 5-1 with a goal at 11:53.
Ottawa was without defenseman Erik Karlsson, who had played 324 consecutive games. The Senators captain is day to day with an upper-body injury sustained in a 3-2 shootout loss at the Philadelphia Flyers on Tuesday. He leads the Senators with 15 goals and 68 points.
"He's our best player, hands down, there's no questions asked about that," Ottawa goalie Craig Anderson said. "But at the same time it's an opportunity for other guys to play minutes and make plays."
Montreal defeated the Florida Panthers 6-2, Toronto defeated the Nashville Predators 3-1, and Boston shut out the Dallas Stars 2-0.