Carlson signed a two-year, $17 million contract ($8.5 million average annual value) with Tampa Bay on July 1.
Anthony Cirelli scored, and Nikita Kucherov had two assists for the Lightning (3-1-0), who won all three games of their homestand. Dennis Hildeby made 34 saves in his debut with Tampa Bay after being acquired from the Toronto Maple Leafs on July 1.
Quinn Hughes had a goal and an assist and Blake Coleman also scored for the Wild (2-1-1), who have lost two in a row. Jesper Wallstedt made 32 saves.
Cirelli gave Tampa Bay a 1-0 lead at 5:26 of the first period when he scored on a redirection Erik Cernak’s point shot.
Carlson’s goal 36 seconds later extended it to 2-0. He scored on a wrist shot from the point that got past Wallstedt with Gage Goncalves providing a netfront screen.
Hughes cut it to 2-1 at 2:32 of the second period, scoring on a shot from the center point that got through traffic and past Hildeby.
Carlson’s power-play goal made it 3-1 at 4:55, a one-timer from the high slot off a pass from Kucherov.
Coleman cut it to 3-2 at 14:01 on the power play, beating Hildeby high glove side from the left circle with Kirill Kaprizov providing the setup pass.
