It was Bozak's sixth goal in the past four games, and Toronto is 2-for-2 on its five-game homestand.
"I think I'm used to it now," Bozak said about the discussion regarding his spot on the Maple Leafs' depth chart. "It's been five years of the same thing over and over again. I'm surprised they don't get sick of talking about it.
"I'm playing where I am, the team is doing well, and I am doing well. Hopefully we can just stay consistent and keep it up."
Bozak is solid in the faceoff circle, smart at both ends of the ice and is the line's defensive conscience.
Toronto got control of the puck off the opening faceoff, worked it into the Dallas zone, and Bozak scored on the first shot, beating Kari Lehtonen at 27 seconds.
Toronto made it 2-0 at 15:16 when center Nazem Kadri took a drop pass from right wing Mike Santorelli and wristed a shot from the top of the left circle that hit the near post before entering the net. It was Kadri's sixth goal of the season and first in five games.
The Maple Leafs (13-8-3) opened the second period on the power play and took advantage, going up 3-0. With Hemsky in the penalty box for slashing, Kessel's low snap shot from 20 feet found its way past Lehtonen at 56 seconds.
A minute after a Kessel shot hit the crossbar, Toronto left wing Joffrey Lupul scored his fourth goal of the season when he put a rebound past Lehtonen at 9:31.
Dallas left wing Ryan Garbutt, who returned form a two-game suspension for kneeing Taylor Hall of the Edmonton Oilers, scored his fourth goal of the season at 2:11 of the third period. With each team playing a man short, Garbutt got a rebound in front of the net and stuffed it past Bernier.
Lupul responded with his second when he found himself standing at the side of the goal with Lehtonen down. The puck squirted to Lupul and he tapped it in at 5:20.
The Stars (9-11-5) had an opportunity to get back into the game when they were given a two-man advantage for 1:30 at 7:23 of the third period but they failed to attempt a shot on goal during the power play.
Dallas did score again at 15:25 when Hemsky, standing in front of the Toronto net, took a pass from Shawn Horcoff behind the goal and put a high shot past Bernier.
Stars left wing Erik Cole said falling behind in the first minute of the game put his team behind the 8-ball.
"We had to play catch up all night," Cole said. "It's hard enough to win games when you give the other team two- and three-goal leads. We're working hard, but we still need to do a lot of things better with the puck. We did a lot of good stuff tonight, but there is still a lot more we could do and we could make fewer errors."
Cole said he still believes in the Stars.
"We can be a great team," Cole said. "I have seen us play great games through stretches through the season, just not consistently enough. It's here, but we need to figure it out and play the game that is going to make us successful as a group. When we play our game we can frustrate other teams and we won't give as much on offense and it'll take pressure off our goaltending."
The Maple Leafs host the New Jersey Devils on Thursday.