Kucherov, who also had an assist, won it on a wrist shot from the slot, beating Calvin Pickard glove side.
Kucherov’s goal came after Charle-Edouard D’Astous tied it 3-3 at 16:29 of the third period with a 6-on-4 goal on the power play with goaltender Dennis Hildeby pulled for the extra attacker.
Jake Guentzel had two goals and an assist, and D’Astous also had two assists for the Lighting (11-3-2), who won their third game in a row and extended their point streak to six games (4-0-2). Hildeby made 19 saves.
Maxim Shabanov scored twice, and Blake Coleman also scored for the Wild (12-3-4), who had won three in a row but extended their point streak to eight games (6-0-2). Pickard made 30 saves.
Minnesota was coming off a 4-1 win against the San Jose Sharks on Friday.
Coleman gave Minnesota a 1-0 lead just 55 seconds into the game. He skated into the zone and fired a wrist shot, tucking the puck into the corner of the far post.
Shabanov’s power-play goal extended it to 2-0 at 2:58 on a backhand shot in front.
Guentzel cut it to 2-1 at 16:34 of the second period, knocking a slap shot under Pickard’s glove with 23 seconds remaining on a four-minute man-advantage.
Shabanov scored again to make it 3-1 at 6:49 of the third period. He went up the ice, skated past the defense and buried a wrist shot five-hole.
Guentzel cut it to 3-2 at 13:44 after tipping Brayden Point’s shot in front.
