Jared Spurgeon, Nate Prosser, Marcus Foligno and Jason Zucker also scored for Minnesota, playing its first game after a five-day break. Matt Cullen had an assist for his 700th career point.
Brayden Point scored twice for the NHL-leading Lightning, who lost a season-high third straight.
Playing the first of eight straight road games around next weekend’s All-Star Game, the Lightning got 30 saves from Andrei Vasilevskiy. He has allowed 23 goals in his past five starts.
Tampa Bay, which has a league-best 65 points, lost 5-1 to Calgary before its bye week and 4-1 to Vegas in its first game back Thursday — both at home.
Minnesota continued its dominance at Xcel Energy Center. The Wild are 6-0-2 at home since Dec. 27, outscoring opponents 32-16.
In his eighth game back after microdiscectomy surgery in October, Parise gave the Wild a 2-0 lead late in the first period by tipping in Ryan Suter’s shot. Tampa Bay unsuccessfully challenged the call, claiming goaltender interference.
Spurgeon scored three seconds into a power play earlier in the first.
Prosser precisely put the puck between Vasilevskiy and the post for a 3-0 lead seven minutes into the second, but Point scored late to get the Lightning within two.
Point scored on a two-man advantage in the third to make it 4-2, a goal upheld after the Wild challenged for goaltender interference.
Cullen, who assisted on Foligno’s goal early in the third to make it 4-1, has 252 goals and 448 assists during his 20-season career.
NOTES: Wild G Devan Dubnyk made 21 saves and is 6-1-1 in eight games since missing six with a lower-body injury. He is 9-0-2 at home since Nov. 14. … Tampa Bay has two wins all-time in Minnesota, the least amount of road wins against a single team. Its last one was April 2, 2011. . C Kyle Rau had an assist in his Wild debut. Recalled on Friday from AHL Iowa, he signed with the team in the off-season after playing 33 games with Florida over the past two seasons.
Lightning: At the Chicago Blackhawks on Monday.
Wild: Host the Ottawa Senators on Monday.