Joe Pavelski scored for Dallas (4-1-0). Anton Khudobin allowed four goals on 16 shots before being replaced in the second period by Jake Oettinger, who made 10 saves.
"I don't blame [Khudobin]," Stars coach Rick Bowness said. "It was the five guys in front of him and the four guys on the penalty kill. We just didn't play very smart and we didn't play hard enough."
Trocheck scored from in front off a backhand pass from Necas to give the Hurricanes a 1-0 lead at 4:05 of the first period. Steven Lorentz, who was playing his second NHL game, got his first NHL point with the secondary assist on the play.
"[Trocheck] has been great, and that's one of the reasons we got the win tonight," Brind'Amour said. "He was really good. You can't say enough about it. That center position is so important."
Trocheck scored the first of three straight Carolina power-play goals to make it 2-0 at 6:55, getting to the rebound of his initial tip in front.
"I thought our power play has been real good this whole start to the season," Trocheck said. "We're moving the puck really well, getting our looks. It was just a matter of time before they started going in."
Andrei Svechnikov scored his fourth of the season when he took a pass from Aho and tucked in a backhand for a 3-0 lead at 8:42 of the second period. Ryan Dzingel extended the lead to 4-0 at 10:21, gathering a cross-ice pass from Necas and scoring from low in the right circle.