Filip Gustavsson made 19 saves for the Wild, who snapped a three-game losing streak in the finale of a two-game road trip.
The Wild went in front to stay 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.
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.
The Wild failed to convert six power-play opportunities.
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.
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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Scott Charles, The Associated Press