Teuvo Teravainen scored for the Hurricanes (45-16-8), whose point streak ended at six games. Frederik Andersen made 16 saves. Carolina leads the New York Rangers by five points for first place in the Metropolitan Division.
"I have no qualms about the way we came out and played tonight," Hurricanes coach Rod Brind'Amour said. "That's a good team. I know we didn't give up that much and that's really the key."
Zuccarello's power-play goal gave the Wild a 1-0 lead at 10:20 of the first period. He scored on wrist shot from above the left face-off circle.
"'Zuc' decided to take all the responsibility all to himself for that one," Kaprizov said. "I gave him a pretty innocent pass and he did the rest. Thanks to him, and of course, it was special."
Kulikov made it 2-0 at 4:10 of the second period when he scored off a backhand feed from Tyson Jost.
Fleury faced 15 shots in the second period. The 37-year-old made a shoulder save on Brady Skjei in close, stopped Nino Niederreiter cutting through the slot and made a blocker save on a one timer by Martin Necas.
"They have different guys coming and a lot of guys at the net for tips and rebounds and screens," Fleury said. "Those are hard sometimes because they're always moving. But I thought our guys kept it on the outside and had good sticks to defend those plays much of the time."
Brind'Amour played six seasons against Fleury in the NHL.
"Tonight, the thing that gets overlooked, there were about three that were tipped, and he made the adjustment off the tip, which doesn't happen very often with goalies," the Hurricanes coach said. "He is quick enough still to make the adjustment. That was impressive to see."
Kaprizov scored from a sharp angle inside the left post for a 3-0 lead at 7:24 of the third period.