At 8-4-0, the Coyotes are off to their best 12-game start since going 9-1-2 in 2000-01. Bryzgalov improved to 7-3-0.
Bryzgalov stopped 11 shots in the third period and made four big late saves after the Blues pulled goalie Ty Conklin for an extra attacker.
"They came out with everything they had near the end, you've got to expect that," Bryzgalov said. "Fortunately, we were able to get the job done and hold on."
Bryzgalov also shut out Stanley Cup champion Pittsburgh 3-0 on Oct. 7 and blanked San Jose 1-0 in a shootout win Oct. 12. He established a career shutout string of 137:46 from October 10-15. Bryzgalov has 11 career shutouts -- nine with Phoenix.
"He's phenomenal. He comes up big all the time," Winnik said.
Winnik opened the scoring in the second period, slipping a wrist shot past Conklin's stick side. It was Winnik's second goal of the season and his first since the Coyotes' season-opening win at Los Angeles on Oct.3.
"Just trying to put it on net and make something happen," Winnik said.
Pyatt scored his first of the season early in the third period.
Vernon Fiddler assisted on both goals.
The Coyotes have outscored their opposition 22-16 during the 6-2 run, which came after a 2-2 start to the season.
"It was a hard fought game," Phoenix coach Dave Tippett said. "That's what I think the identity of our team is -- we're going to score by committee and get good goaltending that gives us a chance to win.
St. Louis (5-5-1) lost for the third time in five games. The Blues have not scored on their last 20 power-play chances and wasted a 25-second 5-on-3 advantage in the first period.
"There were certainly scoring chances there that we should have buried," St. Louis coach Andy Murray said. "We didn't get the job done."
Bryzgalov's biggest save came in the closing seconds of the second period when he slid across the crease to stop a Jay McClement's close-range shot.
"A lot of saves, he was excellent," St. Louis defenseman Eric Brewer said. "We just couldn't get nothing by him."
The Blues fell to 1-4 at Scottrade Center after going 23-13-5 at home last season.
- St. Louis hasn't won consecutive games since sweeping Detroit in Sweden in its first two games.
- Brewer, making his first appearance for St. Louis since suffering a back injury in December, played 17:51 and blocked a shot in the first period. He missed the previous 64 games.
- The Coyotes have allowed a Western Conference-low 23 goals.
- St. Louis winger B.J. Crombeen appeared in his 100th NHL game.