GLENDALE, Ariz. -- Adam Burish celebrated his birthday in style Tuesday night.
"That was fun," said Burish, who also had a pair of assists. "It's nice to get your first one, and on your birthday's pretty neat."
Burish was playing in place of Patrick Kane, who missed his second successive game with a high right ankle sprain.
"The guy I feel bad about right now is Kaner," Burish said. "I'm not sure how he's going to get his spot back. He's going to have to fight me for it."
Huet earned his second shutout this season and the 19th of his career.
"They couldn't do anything to get a goal," Burish said. "Huey was making saves he wasn't even seeing."
Jonathan Toews had two late goals and an assist, and Kris Versteeg, Ben Eager and Colin Fraser also scored for the Blackhawks, who swept the season series against Phoenix, 4-0, for the first time since the 1988-89 season when the Coyotes were still the Winnipeg Jets.
"It was a game that we wanted to get off on a good start on this trip," Blackhawks coach Joel Quenneville said. "Guys have been really diligent in their preparation for this trip. It was exactly like that. No matter who the opposition is, we want to make sure we're consistent in our game and today we were."
Chicago outscored coach Wayne Gretzky's team 20-4 this season.
"They're a pretty good team, first of all," Gretzky said. "They play hard and thank God we're done with them."
The Blackhawks have won 11 of 13 overall, outscoring opponents 55-24 along the way.
Mikael Tellqvist, making his third start in four games, allowed four goals on 13 shots and lasted only one period before he was replaced by Ilya Bryzgalov.
The Coyotes lost their second successive game, both shutouts.
"We have to come out on a mission next game and make sure that come the first period we're ready and we're going to score," Phoenix wing Kyle Turris said. "If somebody has to eat a post to put it in the net, then that's what we're going to do."
Burish opened the scoring at 11:46 of the first on a shot over Tellqvist's right shoulder from the bottom of the left circle. Versteeg made it 2-0 at 14:22 after Tellqvist had slowed Toews' shot from the right side with his glove from the top of the crease. The puck dropped behind the goalie a foot from the goal line and Versteeg swept it into the net.
Fraser was credited with a goal 38 seconds later when Burish's pass deflected off the center's left skate as he skidded to a stop barely inside the crease.
Eager capped Chicago's four-goal first at 16:22 on a long rebound.
Toews scored his first goal with 1:14 left in the second on a rebound off a shot from the low right slot by Martin Havlat.
Toews added his second with 5:12 remaining when he stole the puck from Zbynek Michalek barely inside the Coyotes zone, took two strides and scored on a sharp wrist shot.
"I think we're mature enough to take it one game at a time and not get ahead of ourselves," Toews said. "We went out there and took it one period at a time and got the win. Now it's time to build on that win."
The Blackhawks outscored the Coyotes 10-0 in the first period this season. ... Burish's previous goal came April 4, 2008, against Nashville. ... Phoenix went 0-for-7 on the power play, extending its scoreless streak with the man advantage to 27 tries spanning five-plus games. ... Chicago played without leading scorer Patrick Kane, who missed his second successive game with a high right ankle sprain. ... Phoenix is 2-2 in its past four home games after starting the season 11-3-2 at home. ... Coyotes defenseman Ed Jovanovski left midway through the third when he was punched by Matt Walker, opening a cut above his left eye.