Brian Rolston also scored for Minnesota, which tied a season high with its eighth straight home win. It was just the second time in that stretch the Wild won by more than one goal.
Minnesota, which entered the night tied with Calgary atop the Northwest Division, is an NHL-best 17-3-1 at home and hasn't lost at the Xcel Energy Center since Dec. 1.
Jon Sim scored with 22.3 seconds left for Atlanta, which looked sluggish in the final game of a four-game road trip. The Thrashers, who won 3-2 in overtime at Ottawa on Monday, finished with just 15 shots on goal, their lowest total since getting 11 on opening night.
Rolston beat Kari Lehtonen with a slap shot on the power play 2:54 into the game. Rolston, named the team captain for January, has four goals and three assists in his last three games.
Parrish scored his seventh goal in six home games late in the first for a 2-0 lead.
Five seconds after a penalty expired, a partially fanned shot by Bouchard was deflected by Atlanta's Marian Hossa to Parrish all alone in front. He easily beat Lehtonen, who went down on Bouchard's shot.
If not for Lehtonen, the margin could have been even worse. He stopped 30 shots in the loss, including several point-blank attempts as the Thrashers' defence struggled to keep the Wild out of prime scoring range.