Kostitsyn, who assisted on Plekanec's goal in the second, put a rebound past Ilya Bryzgalov for his third goal in two games as the Canadiens improved to 5-2-1. Cammalleri also had a goal and an assist.
"All three guys, I think, are in top shape and we feel good with each other," Kostitsyn said.
The line has combined to score 11 of Montreal's 20 goals.
"I was excited coming into this year about our line," Cammalleri said. "I thought that as a group we played with a lot of different combinations last year, not knowing one another, and by the end of the year I felt like us three kind of settled in and found ways to complement one another. I'm a big, big believer that the longer you stay together and the more chemistry you can build the more dynamic you can be offensively.
"I'll reference the Sedin twins [Vancouver's Henrik and Daniel], these guys have played every shift of their lives together and they just seem to know where each other is a second ahead of the defender and the puck ends up in the net more often than not, so that's kind of the idea."
Price, who has started each of the Canadiens' games, made 27 saves for his second straight win, including his first shutout in nearly two years Saturday in a 3-0 win in Ottawa.
Bryzgalov stopped 26 shots.
The Coyotes have not won in Montreal since a 5-4 victory on Oct. 28, 1996.
"Well, you know what? It's a good rink, good fans," said Morris, who scored on a power play 1:01 into the third to draw Phoenix even at 2. "They probably have the best fans in the league. They do a real good job of creating momentum for their team. Even if the team doesn't really have a good play they're always oohing and ahhing on a play that's a close play and I think that they feed off of that. The team plays really well at home and they played well tonight."
Price stuck out his glove to get a piece of Adrian Aucoin's slap shot from the right faceoff circle on another Coyotes power play later in the third.
"He was seeing pucks well, obviously," Aucoin said. "I think on a few of our chances we screened him pretty good and he still made the save. A couple of pucks just hit him without him seeing them and that's when you know your goalie is playing the way you want him to, he's just in the right spot. On my chance, there was a guy diving in front of me so I'm pretty sure he knew I was going upstairs and made the right save."
Turris gave the Coyotes a 1-0 lead 2:49 into the second with his third goal in two games. He scored his first two goals of the season in a 4-3 overtime loss to Carolina on Saturday night.
Montreal scored twice in 2:09 later in the period to go up 2-1. Cammalleri assisted on Plekanec's goal at 7:14 before adding the Canadiens' second power-play goal of the season at 9:23.
Coyotes captain Shane Doan, Price's second cousin, sat out the final game of a three-game league suspension for his blindside hit on Anaheim's Dan Sexton. He is eligible to return Tuesday night in Ottawa.