It was the season opener for each team.
Kirill Kaprizov and Nick Foligno also scored, and Jesper Wallstedt made 19 saves for the Wild.
Roman Josi scored to open his 16th season with the Predators, passing David Legwand (15) for the most in franchise history. Juuse Saros made 27 saves.
Foligno put Minnesota ahead 1-0 at 9:35 of the first period. A rebound off a shot from Michael McCarron was slowed by diving Nashville forward Matthew Wood to the high slot, where Foligno collected it for a wrist shot glove-side.
Coleman made it 2-0 on a power play at 13:48, taking a pass from Bobby Brink and going backhand-forehand over Saros' right pad from in tight.
The forward had been acquired from the Calgary Flames along with defenseman Olli Maatta for three NHL draft picks and defenseman Jake Middleton on July 2.
Yakov Trenin appeared to extend the lead to 3-0 with a shot in off the left post at 15:05, but the goal was overturned after the Predators successfully challenged that Ryan Hartman interfered with Saros.
Josi cut the deficit to 2-1 at 9:23 of the second period. Filip Forsberg sent the puck into the right face-off circle, where Josi one-timed it from a sharp angle off Wallstedt's glove just three seconds after a power play expired.
Coleman had a chance to score again after taking a pass from Matt Boldy on a 2-on-0, but was denied by a pad save from Saros at 11:33.
Kaprizov pushed the lead to 3-1 at 4:42 of the third period by tipping a point shot from Quinn Hughes.
