Wild forward Zac Dalpe tied the game 2-2 at 2:27 of the third period, and Staal scored his second at 11:53, through a screen by Zach Parise.
In his first season with the Wild, Staal leads Minnesota (3-1-0) with three goals in four games. He had 13 goals in 83 games last season with the Carolina Hurricanes and New York Rangers.
"I never felt like I forgot how to play," Staal said. "I knew I could play and I've been in this league a long time. But I needed to come here [to Minnesota] and be ready in training camp, and be fit and hungry. I've done that, and now it's about continuing to build. It's only been four games. I've got a long way to go, but it's been a good start for me and hopefully this team keeps picking up wins, because that's what it's all about."