Miller was playing in his first game since being acquired by St. Louis in a five-player deal with Buffalo on Friday. In addition to posting a 284-186-57 record in 10-plus seasons, all with the Sabres, Miller entered the game 6-0-0 with a shutout and a 1.15 goals-against average in his career against Phoenix.
"I was pretty anxious and nervous all day," Miller said. "It's a new group of guys and you want to show them what you've got and let them know you're there for them."
The night got off to a rocky start courtesy of an unlucky bounce less than three minutes into the game.
With a teammate skating down the slot, Paul Bissonnette wristed a soft shot toward the net. St. Louis defenseman Barret Jackman, seemingly anticipating a harder attempt, dropped to the ice for the block. But the puck ticked off the prone Jackman's left skate and bounced off Miller's right shoulder and into the net for the goal and a 1-0 Phoenix lead at 2:56 of the first.
"Things like that happen," Miller said. "You need to be able to react quickly enough to recover."
Halpern made it 2-0 at 7:09 of the second, slipping behind Shattenkirk after the Blues defenseman cleared Bissonnette from the front of the crease and scoring off Yandle's pass from the left boards.
But momentum turned quickly in the third.
"Everyone on the team could see Berglund was going to score," Blues coach Ken Hitchcock said. "He was on a 2-on-1 and when it went in everyone jumped up. Once we got that first goal, it was a like the weight was lifted off of everybody's shoulders and they just took off."
Just over four minutes later, Paajarvi rifled a shot past Smith from the middle of the faceoff circle to tie the game with 12:26 to go.
Shattenkirk gave the Blues their first lead of the game with 7:14 left when he took a pass at the point, skated into the left faceoff circle and took advantage of a screen from T.J. Oshie to score his first goal since Jan. 21.
Berglund capped the scoring with an unassisted goal with 1:39 left, jumping on a loose puck after Yandle was apparently tripped between the circles in the St. Louis zone and skating the length of the ice before scoring on a sharp wrist shot.
"I think that in the last few games we've had a lot of chances, but we haven't been able to capitalize," Shattenkirk said. "We did a great job of going down 2-nothing and staying with our game plan."
Jeff Halpern scored his 150th career goal and Bissonnette added his first goal since Dec. 14 for the Coyotes, who have lost four straight and five of six.
"I still look and there are good things that we are doing," said Coyotes coach Dave Tippett, whose team squandered a chance to move from 11th place into a wild-card playoff spot in the Western Conference. "They pushed hard and we couldn't push back."
Smith made 26 saves for the Coyotes.
The Blues have won four straight in Phoenix. ... Shattenkirk's goal was his first since Jan. 23. ... Bissonnette set a career high with his seventh point of the season. ... Ott, who had been the Sabres' captain before the trade, also was making his St. Louis debut. ... St. Louis' power-play goal was its first in its past 28 chances. ... Phoenix has surrendered the lead in five of its past 11 games.