Steven Stamkos gave Tampa Bay a 3-2 lead at 14:22 of the third period. Sergachev's initial pass to Stamkos in the slot hit off two Wild defenders and ricocheted near the right post, where Stamkos shot it into the net off the chest of Ryan Hartman.
"It was a good puck possession breakout," Stamkos said. "A little bit of a broken play. For all the good plays that don't go in you are rewarded for one like that."
Kucherov scored an empty-net goal at 19:43 for the 4-2 final.
"I thought we played pretty good," Fleury said. "That's a good team and we hung with them. It's a tough loss for sure."
Prior to the game, Tampa Bay honored Stamkos for scoring his 500th NHL goal in a 5-2 win at the Vancouver Canucks on Jan. 18.
The tribute included a video message from Washington Capitals forward Alex Ovechkin and Pittsburgh Penguins center Sidney Crosby, the other two active players in the League with at least 500 goals.
"It's great to be at home and celebrate that with my family, my teammates, the coaching staff. They were great tonight," Stamkos said. "Obviously, a ton of respect for those guys. Those guys are legends in our game, and to be one of the three active guys with those two guys is pretty surreal."
NOTES:Tampa Bay is one game shy of tying its record for longest home winning streak (11 from Dec. 23, 2019, to Feb. 15, 2020). ... Stamkos extended his goal streak to four games (six goals) and his point streak to nine (seven goals, six assists). ... Vasilevskiy has played 399 games, the second-fewest needed to reach 250 wins in NHL history (Ken Dryden, 381). … Eriksson Ek has six points (three goals, three assists) during a four-game point streak. … Minnesota has scored eight short-handed goals this season, second in the NHL to the Philadelphia Flyers (nine).