Gustavsson stopped 27 shots for his sixth career shutout. Ryan Hartman had a goal and an assist, and Jon Merrill and Jacob Lucchini also scored.
Minnesota has won four of its last five and picked up a point in its eighth straight game, going 6-0-2.
John Gibson made 28 saves as the Ducks dropped their seventh straight and were blanked for the third time in four games, including a 2-0 loss at Minnesota on March 14.
It’s the first time in the Ducks 30-year franchise history they have had two losing streaks of at least seven games in the same season. They had an eight-game skid in November after starting the season with nine wins in its first 15 games.
After the Wild scored twice in the opening two minutes of the second period, Kaprizov made it 3-0 11:50 into the period on a power play when he jammed in the puck with plenty of traffic around the net. He has scored a goal in five straight games, and has 10 goals and 14 points during his point streak.
Kaprizov is in his fourth season with the Wild. He reached 150 goals in 265 games, the fastest of the four players in franchise history to reach the milestone.
Hartman put in a rebound 35 seconds into the second period after Gibson made a pad save on a shot by Marcus Foligno. It was Hartman’s 18th of the season and his third in five games.
Merrill made it 2-0 at 1:56 with a wrist shot near the boards just outside the left faceoff circle that went off the far post and into the net. In his third NHL game, Marat Khusnutdinov picked up his first point with an assist.
Lucchini scored his second of the season 13:03 into the third on a two-on-one break.
Up next
Ducks host the Chicago Blackhawks on Thursday night.