A big three-point play off a post up by Nikola Pekovic with 48.6 seconds left broke a 91-91 tie and put the Wolves in the driver's seat in the game's closing moments.
After a stop, Thaddeus Young hit a runner off great ball movement to put the Wolves up five at 96-91, and the Wolves made a pair of free throws down the stretch to put it away.
Minnesota took an early lead against the Nets, but squandered a 15-point first quarter advantage to trail at the half 48-46. But they fought back in the second half and won it thanks to the strong finish.
Pekovic and Ricky Rubio each finished with a double-double. Pek posted 16 points and 11 rebounds, while Rubio had 14 points to go with 12 assists. It was his drive to the rim that resulted in a layup that tied the game at 91.
Kevin Martin had a big game, leading the way for the Wolves with 24 points, including four three-pointers. Rookie Andrew Wiggins scored an efficient 17 points on 7-of-12 shooting. He also grabbed four boards.
Joe Johnson had 22 points to lead the Nets, while Deron Williams added 19. Former Wolves star Kevin Garnett scored just two points, but grabbed 11 rebounds for the Nets.
It was a nice way for the Wolves to start a stretch of six games away from home. They don't return to Target Center until Nov. 19.
Minnesota (2-2) plays at Orlando (0-4) on Friday night.