On the winning goal, Holmstrom drove past Matt Boldy toward the net, went to his backhand and pushed a shot through Filip Gustavsson’s pads.
Ilya Sorokin made 33 saves, and Tony DeAngelo had two assists for the Islanders (25-15-5), who have a four-game point streak (3-0-1).
Quinn Hughes had three assists, and Ben Jones scored his first NHL goal for the Wild (26-11-9), who have lost three of their past four (1-1-2). Gustavsson made 23 saves.
Jones, playing his 49th NHL game, gave the Wild a 1-0 lead at 2:51 of the first period when he scored in front with a deflection of a pass from Brock Faber.
Jean-Gabriel Pageau was credited with the goal that tied it 1-1 at 4:18. Minnesota forward Marcus Johansson tried to clear a rebound and inadvertently pushed the puck into the net instead, with Pageau being the last Islanders player to touch it.
Boldy put the Wild ahead 2-1 on a 5-on-3 power play at 15:25. He scored with a one-timer from the right face-off dot off a Hughes feed.
Holmstrom pulled New York back even at 2-2, scoring with a slap shot through traffic at 1:29 of the second period.
Kirill Kaprizov then put the Wild in front 3-2 at 8:26, converting on a snap shot from a sharp angle to the glove side off a cross-ice pass from Daemon Hunt. It was Kaprizov’s 25th goal of the season.
Casey Cizikas tied it 3-3 with a short-handed goal at 19:34. He finished a 2-on-1 off a pass from Holmstrom by putting a backhand around Gustavsson at the right post.