Kaprizov scored on a power play from the left face-off dot to give Minnesota a 1-0 lead at 15:04 of the first period.
Kaprizov has 19 points (eight goals, 11 assists) during his point streak, which is tied with Mikael Granlund (2016-17) and Kevin Fiala (2021-22) for the longest in Wild history.
Hintz tied it 1-1 on a rebound at 6:58 of the second period.
Connor Dewar restored the Wild to a 2-1 lead at 10:42, beating Suter down the right side for a short-handed goal.
Jake Middleton made it 3-1 at 13:17 when his shot from the top of the left circle deflected in off Stars forward Ty Dellandrea, and Jordan Greenway scored 15 seconds later off a net-front scramble to extend it to 4-1.
"It was a roller coaster," Minnesota forward Ryan Reaves said. "I think they carried a decent amount of the first period, and obviously we had a good push in the second. Start off well in the third. Good teams, they find ways to battle back. Hats off to them, they're a good team and they're going to find ways to push and claw back in that game. We found a way to come up with a win."
NOTES:Hintz's hat trick was his second in the NHL. … Robertson has 41 points (23 goals, 18 assists) in 25 games. Only Dino Ciccarelli (22 games in 1986-87) and Bobby Smith (23 in 1981-82) have reached 40 points in fewer games in Stars/Minnesota North Stars history. … Pavelski (38 years, 146 days) had three assists, becoming the third player in Stars/North Stars history to have that many at age 38 or older, joining Dean Prentice (40 years, 65 days) and Sergei Gonchar (39 years, 245 days). … Reaves has three assists in five games since being acquired by the Wild on Nov. 23. He did not have a point in 12 games with the New York Rangers.