The 24-year-old made 19 saves in the first period for New York (26-16-6), which is 4-1-1 in their past six games.
"I think all game he played great," Islanders captain John Tavares said. "He really made some big saves, and got the first [win]. He's worked really hard to get back from injury. He is very talented. Not many people know him since they haven't seen him all year. But for us, shooting on him, seeing him in practice, knowing how hard he worked, he's a great guy and you can see the skill set that he has."
Berube found out on Monday that he would start and kept the Islanders in the game early.
"I think it's better [to see more shots] it got me in the game really quick and I felt really comfortable out there. It was a good game overall," Berube said.
"Everything happened so quick. [The coaches] told me [Monday] at practice, so I didn't have too much time to get ready, but the time in Bridgeport helped me to get focused for this game. ... I have been practicing with the guys all year. ... The play was fast, but the guys did a good job in front of me keeping shots to the outside."
New York scored three goals in the second period, including two in the first six minutes. Mikhail Grabovksi scored with a wrist shot from in close at 3:20 and Anders Lee tipped in a Travis Hamonic point shot at 5:07 to make it 2-1.
Jason Pominville scored with 1:24 left in the second period to tie the game, 2-2. He took a shot from the slot which was denied by Berube, but he got his own rebound and scored.
Brock Nelson answered 42 seconds later, scoring his team-leading 20th goal, and sixth in as many games to give the Islanders a 3-2 lead with 41.5 seconds left in the period.
Minnesota (23-18-9) is 1-7-1 in its past nine games and has scored 14 goals.
"You never want to give one up to start a period or finish a period and that one hurt," Wild forward Zach Parise said. "We have to start winning some games. ... Losing another one again makes it even tougher for us."
Former Islanders forward Thomas Vanek was on the ice for Nelson's goal.