GLENDALE, Ariz. -- The Arizona Coyotes have been preaching patience and small victories with their young core of players. The pups got a little payoff in a 3-0 win over the Vancouver Canucks on Thursday night at Gila River Arena.

Lawson Crouse, Alex Burmistrov and Tobias Rieder scored and Mike Smith made 19 saves for his first shutout this season as Arizona posted its first three-game winning streak of the season.

"When you win it's a good feeling around the room," Coyotes coach Dave Tippett said. "We had five rookies in the lineup and all five of them contributed tonight. They're turning into good NHL players."

The shutout was the 31st of Smith's career and his 20th as a Coyote -- one shy of the franchise record held by Nikolai Khabibulin and Ilya Bryzgalov -- allowing Smith to head to the NHL All-Star Game in style as the team's lone representative.

The Coyotes held the Canucks without a shot in the first period, the fifth time that has happened to the Canucks in franchise history. It was the fourth time in franchise history the Coyotes held an opponent without a shot in a period and it the second time it has happened in the first period. The last time was Jan. 15, 1982, at Calgary.

The Canucks finally managed their first shot on goal off the stick of right winger Alex Burrows with 11:48 left in the second period. Burrows' shot came while the Canucks were short-handed, and it came from his own zone.

"It was pretty boring there for a period and a half," Smith quipped. "That just goes to show what we did in front of me tonight. A lot of credit goes to our group. We really wanted to win this game and get on a little bit of a roll. We've played a lot better as of late and done a lot of good things. The work we've put in got rewarded tonight."

The Coyotes opened the scoring just seconds after Smith made a left pad save on Henrik Sedin off a redirect in front of the Coyotes net. Arizona defenseman Oliver Ekman-Larsson sent a shot toward the net that Ryan White deflected wide but onto the stick of Crouse.

Crouse used all of the reach in his 6-foot-4 frame to score on a wraparound before goalie Ryan Miller (28 saves) could get to the left post at 12:56 of the second period for 1-0 lead.

"They've played well at home lately," Canucks coach Willie Desjardins said of the Coyotes, who have won five of their last six games at home. "But it doesn't matter how well a team is playing. You still should be able to get stuff to the net. The first three minutes we had some real good chances and didn't hit the net. We didn't have much after that."

Miller entered the game with a sparkling 11-1 career record against the Coyotes, a 1.40 goals-against average, two shutouts and a .954 save percentage, but the Coyotes got to him again during a four-minute power play in the third period.

Burmistrov gave Arizona a 2-0 lead at 4:29 of the third period when he picked off a clearing attempt by the Canucks' Michael Chaput. With Miller out of position after an initial save on Radim Vrbata, Burmistrov, a Jan. 2 waiver pick-up, scored his first goal as a Coyote to give him six points in six games with Arizona.

Rieder added an empty-netter off a pass from Vrbata with 33.4 seconds left. It was Rieder's third goal in his last three games.

"You've got to give them credit. They came hard at us and we weren't able to answer today," Canucks center Henrik Sedin said. "They didn't give up any outnumbered chances. It was a tough one today."

NOTES: Coyotes LW Max Domi saw a doctor to evaluate the broken bone in his right hand. Coach Dave Tippett said Domi could return practice as soon as Monday and to the lineup in about two weeks. Domi hasn't played since breaking the hand in a fight against Calgary on Dec. 8. ... Coyotes RWs Jordan Martinook (upper body) and Shane Doan (upper body) were in the lineup. Doan missed the last two days of practice; Martinook missed the last two games. ... Coyotes C Brad Richardson (fractured right tibia and fibula) is on injured reserve and out indefinitely. ... Canucks D Philip Larsen replaced D Alex Biega in the lineup. Larsen missed the last 23 games with an upper-body injury. His last game was Dec. 6 at New Jersey. ... Canucks D Ben Hutton (hand) and RW Anton Rodin (IR, knee) are day to day. D Erik Gudbranson (IR, wrist), RW Derek Dorsett (IR, shoulder) and RW Jannik Hansen (IR, knee) are out indefinitely.