Price made 17 saves for Montreal (26-11-6) but allowed seven goals in a game for the fifth time, the first since March 2, 2013 against the Pittsburgh Penguins.
WATCH: All Canadiens vs. Wild highlights
"Regardless of what the score is in any situation, I just try and focus on my next shot," Price said. "Whether it's 7-0 or 1-0, whatever the score is, it doesn't matter to me. It's a very disappointing result, but it's over now, so [we] move on."
Nino Niederreiter scored twice for the Wild (26-9-5), who are 15-1-1 in their past 17 games and are 9-1-0 at home in their past 10.
Tomas Plekanec ended Devan Dubnyk's shutout with nine seconds left in the third period. Dubnyk made 20 saves and is 13-1-0 with 27 goals allowed in his past 14 starts.
"Anytime there's a decimal point on the clock, it stings a little more," Dubnyk said of not getting the shutout. "Obviously wins are tough to get in this League and you've got to enjoy them. Shutouts are a bonus. Not going to lose any sleep over [it] tonight. That's about as good a game as you get, I think.
"I was happy I was on my end. I felt like every shot we got was a scoring chance down there. Guys were more than solid for me in my end and allowed me to feel comfortable all game."
Christian Folin scored his first goal of the season at 2:34 of the first period to make it 1-0.
The Wild scored three goals in the second period, two 39 seconds apart: by Staal at 6:35 to make it 2-0, and by Jordan Schroeder, who dove to deflect a Jared Spurgeon shot at 7:14.
Staal has eight points (three goals, five assists) in a four-game point streak, and 20 points (eight goals, 12 assists) in his past 14 games, including a point in 13 of those 14.
Niederreiter scored the fourth goal for Minnesota at 17:58.
Price started the third period after allowing four goals on 14 shots in the first two. Montreal, with Al Montoya in goal, defeated the Winnipeg Jets 7-4 on Wednesday.
"Carey wanted to stay there [after the second period] and I respected the decision, and even more I think I appreciate the fact that you want to stay there," Canadiens coach Michel Therrien said. "It's one of those nights where it's a tough night and we're all in this together and we're all suffering as a team. Pretty simple."
Jason Zucker redirected a shot by Spurgeon on the power play at 3:31 of the third period to make it 5-0. Ryan Suter scored a power-play goal at 6:06, and Niederreiter scored his second at 14:26.
"Whatever it is [we're doing] I'd like that to continue because we're not going to score seven goals in this league every night," Wild coach Bruce Boudreau said. "We have good balance where different guys are scoring all the time, which is a positive thing."
