Filip Gustavsson made 19 saves for the Wild, who snapped a three-game losing streak in the finale of a two-game road trip.
''There was some urgency in our game,'' Wild coach Dean Evanson said. ''We didn't get frustrated tonight. We stayed the course, we shot the puck a little bit more.''
Scott Mayfield scored for New York, and Ilya Sorokin finished with 33 saves. It was the Islanders' fourth consecutive loss.
The Wild went in front with two goals in 93 seconds in the third.
Gaudreau tied it at 1 when he scored a short-handed goal at 10:55. Sorokin was able to get his glove on the puck, but not before it crossed the goal line upon video review.
Joel Eriksson-Ek sidestepped Islanders forward Jean-Gabriel Pageau and assisted on Gaudreau's 10th of the season.
''In every situation, all three zones, they are strong, good, they play a smart system,'' Gaudreau said of the Islanders. ''They are one of those teams that can be frustrating to play against.''
Steel then gave Minnesota a 2-1 lead at 12:28 off a nice setup by linemate Mats Zuccarello. Kaprizov recorded the secondary assist and picked up his 50th point of the season.
Kaprizov added an empty-net goal at 18:48.
Gustavsson made a critical save five minutes into the third period, denying a one-timer from Simon Holmstrom after Minnesota defenseman Jon Merrill turned the puck over in the defensive zone.
The Wild failed to convert five power-play opportunities.
''You don't want to be in the box that much,'' Islanders forward Josh Bailey said. ''For the guys that aren't killing penalties, they are getting cold on the bench sitting there, then there are TV timeouts. It's nothing we haven't experienced before but it does take away from the rhythm of the game.''
Mayfield opened the scoring 16:49 into the first with his fifth goal, matching his career best from the 2018-19 season. The bruising defenseman sent a long wrist shot past Gustavsson.
It was the first time the Islanders had scored first since Dec. 29 against Columbus. It also was the 26th goal by an Islanders defenseman this season.
''Defensively, we were not bad at all,'' Gustavsson said. ''We were really good defensively. Their best chance was a breakaway in the second period but other than that they had shots from outside.''
HELP ON THE WAY
Islanders defenseman Adam Pelech practiced with the team prior to the game against the Wild for the first time since sustaining an undisclosed injury on Dec. 6 against St. Louis. Pelech skated on his own for the previous three days. ... Islanders forward Kyle Palmieri also is close to returning. He traveled with the team on its recent four-game trip. Palmieri left the game against Arizona on Dec. 16 with an upper-body injury. He has missed 22 of the previous 23 games.
Wild: Host the Arizona Coyotes on Saturday.
Islanders: Host the Montreal Canadiens on Saturday.
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