McDonald scored a power-play goal on a hard shot from the crease, with Wild goaltender Niklas Backstrom partially screened, handing the Isles a 1-0 lead 9:05 into the game.
Nielsen struck less than 3 minutes later, tipping in Mark Streit's slapper from the point past Backstrom.
The Islanders' Al Montoya turned aside 20-of-21 shots, including all 10 he saw in the middle frame.
Matt Cullen scored for Minnesota, which managed only two shots on goal in the first period.
Backstrom ended up stopping 12-of-14 shots.