Nick Bjugstad and Nico Sturm scored, and Kaapo Kahkonen made 24 saves in his season debut for the Wild (4-1-0), who defeated the Anaheim Ducks 4-3 in overtime Saturday.
"Our energy has been real good up to this point. For whatever reason, we had nothing there tonight," Minnesota coach Dean Evason said. "To put a finger on it, I don't know. They played last night, too. we should have had more than we had tonight."
Josi gave Nashville a 1-0 lead at 3:45 of the first period with a power-play goal, scoring on a rebound in the slot after his initial deflection was blocked.
The Wild have allowed the first goal in each of their five games.
Johansen scored a power-play goal on his own rebound in front to make it 2-0 at 5:54. He then pushed the lead to 3-0 at 12:25 when he scored after receiving a spinning pass from Josi.
Bjugstad cut it to 3-1 at 11:30 of the second period when he took a stretch pass from Jon Merrill off the boards and beat Ingram blocker side from the right face-off circle.
Forsberg deflected Josi's one-timer from the point to make it 4-1 at 13:15, and Tanner Jeannot batted the puck out of the air to extend the lead to 5-1 at 18:35.
"[We] definitely wanted to keep going and not let them come back," Josi said. "We knew how dangerous they were. Although they got the first goal in the second, I thought we did a good job still creating chances, still being aggressive, and I think that was key."