Matt Boldy scored the go-ahead goal early in the third period and had an assist for the Wild (5-0-2), who have won four in a row during their point streak, which matches the longest to open a season in their history (2008-09). Marc-Andre Fleury made 23 saves.
"We're maybe more on the same page, everywhere and in every zone," Fleury said. "Guys know where to go, where they'll be, so when we get the puck, they don't have to think or look around too much. We have an idea where the guys are at, and that allows us to move quicker and get out of the zone quicker and attack a little quicker in the offensive zone."
Nikita Kucherov and Brandon Hagel scored for the Lightning (4-3-0), who have lost three of four. Andrei Vasilevskiy made 14 saves.
"That’s a good team over there," Tampa Bay forward Anthony Cirelli said. "They stuck to their structure the whole game. They capitalized on their chances and played a simple game. For us, I thought we had spurts of playing our game, but at times we got away from it, and they took advantage of that."
Kaprizov gave Minnesota a 1-0 lead at 6:23 of the first period. He scored on a one-timer that beat Vasilevskiy short side off a cross-ice pass from Marco Rossi.