Nick Ritchie, Loui Eriksson and Alex Galchenyuk scored, and Karel Vejmelka made 46 saves for the Coyotes (22-49-5), who have lost seven straight while being outscored 43-10.
"It's tough for sure, you're always trying to find a solution," Arizona coach Andre Tourigny said. "The NHL is not an easy league … but we'll keep pushing."
Trocheck made it 1-0 at 4:01 of the first period, redirecting Brady Skjei's centering pass off the rush, and Fast extended the lead to 2-0 at 1:47 of the second period.
Domi made it 3-0 at 4:43, scoring off a rebound of Niederreiter's shot for his 100th NHL goal, and his first in 14 games since being acquired from the Columbus Blue Jackets on March 21.
"It's special to play a game in this League and score one goal, so [when] you get 100 it's a special feeling for sure, and to do it back here was great," said Domi, who was selected in the first round (No. 12) by the Coyotes in the 2013 NHL Draft and played his first three NHL seasons with Arizona from 2015-18.
With forward Jordan Staal out day to day with an upper-body injury sustained against the Colorado Avalanche on Saturday, Domi played on a line with Niederreiter and Fast.
"He was moving his feet pretty well, that's definitely a big key for his game," Niederreiter said. "It's easy to play with him. We talked a lot with him on the ice and off the ice and tried to get him going that way a little."
Carolina coach Rod Brind'Amour said he liked how all four lines were active and productive, but especially the reconfigured line with Domi in the middle.
"Obviously with 'Jordo' out, that's a big, big hole there and I thought Max, [and] it's asking a lot of him to play in that spot, did a nice job," he said.