Pacioretty got his first goals in 10 games since Oct. 12 in Vancouver, although he missed eight games with a leg injury during that stretch.
"There's a lot of things probably being said about me out there. That's how it is in this business when you're not performing," said Pacioretty, who had been criticized for being a "perimeter" player of late, among other slights. "Everyone goes through it, but it felt good tonight.
"You can look at stats all you want but I missed a lot of good opportunities lately. One game I had eight shots. It started getting into my head, thinking that I can't score, so it's definitely a monkey off the back. The first one was lucky, off a skate and in, but you take them as they come."
Desharnais had two assists, giving him three points in 20 games this season. Only last week, newly elected Montreal Mayor Denis Coderre caused a stir when he suggested Desharnais be sent to the minors. He was scratched for one game, but bounced back with better efforts of late.
When he is on his game, the stocky center is a clever passer and playmaker, although he seems to click best with Pacioretty.
Part of the breakthrough came when coach Michel Therrien put tenacious right wing Brendan Gallagher on their unit. That threesome was Montreal's best line in the second half of last season.
Pacioretty went hard to the front of the net for two of his goals Tuesday.
"Davey and I, our chemistry is at a level where he knows where I'm going and he can throw blind passes, and that's what happened," Pacioretty said.
"Gally gets everyone going," he added. "He's an energetic player. With him getting into the forecheck and disrupting the defense a little, all it takes is a split second. He's a hound on the puck and he got us going."
Minnesota looked nothing like the air-tight defensive club that was piling up wins in recent weeks. Once Pacioretty's first goal went in, the Wild put up little fight. Top defenseman Ryan Suter ended the night minus-3, while his partner, Jonas Brodin, was minus-4.
Minnesota coach Mike Yeo wants to see his team push back Wednesday night in Ottawa.
"It's all a matter how you take this one in," Yeo said. "If we just sit here and say, `We've been on a nice run and this was bound to happen,' then I don't think we should expect much difference from tonight.
"If this stings like it should, it should be motivating for us to win that game."
Kuemper looked shaky in allowing three goals on nine shots.
Yeo said pulling Harding was partly to keep him fresh to play in Ottawa. Harding has given up three goals only twice this season, both times to Montreal.
Pacioretty's slump ended at 2:57 of the second period when Desharnais' pass went in off his skate from in front of Harding.
The Canadiens, coming off a 1-0 loss at home to the New York Rangers on Saturday night, had not scored since Lars Eller's goal at 7:34 of the second period in a 3-2 shootout victory last Friday in Columbus.
Pacioretty converted a spin-around pass from Desharnais at 10:06 at even strength and then ended Harding's night when he tipped in P.K. Subban's point shot on a power play at 13:36.
The only other hat trick of Pacioretty's career came on Feb. 9, 2012.
Bournival came from behind the net and beat Kuemper inside the near post at 16:16. Briere one-timed Brian Gionta's cross-ice pass behind Kuemper on a counter attack 4:42 into the third.
Niederreiter spoiled Carey Price's shutout bid less than a minute later when he went to the net to bang in his own rebound after a feed from behind the net from Kyle Brodziak.
Galchenyuk converted Andrei Markov's feed on a power play at 7:35.
Heatley jammed in a goal on a power play with 1.3 seconds left for his third goal in 22 games.
The six goals were a season high for Montreal, and the most allowed by Minnesota. ... Montreal wing Rene Bourque (lower body) sat out and Ryan White returned to the lineup. ... Douglas Murray and George Parros were scratched. ... Minnesota sat defenseman Matt Dumba. ... The Wild started a four-game road trip that takes them to Ottawa on Wednesday, Winnipeg on Saturday and St. Louis on Monday. ... In 43 career games against Montreal, Heatley has 25 goals and 52 points.