ST. LOUIS — Mike Smith is used to facing plenty of shots, so this was nothing new.
Coming into the game, Smith had seen the most shots of any NHL goalie (516). St. Louis added 39 more to that total, including 13 in the third period.
"It was nice for me to play like that tonight and bail the guys out," Smith said. "I've let in a lot of goals on nights where the guys have bailed me out, so it's nice to be on the other end of the spectrum."
The Coyotes made Smith a winner early in the extra session. Ekman-Larsson, who had an assist on Phoenix's first goal, took a pass from Mike Ribeiro and beat goalie Jaroslav Halak with a shot from just inside the blue line.
"It was a great play there by Ribeiro," Ekman-Larsson said. "I saw (Shane) Doan was coming in from the corner so I shot it, and it was perfect."
With the Blues swarming in the third period, Smith was at his best. He allowed a goal to Roman Polak that tied the game but made 12 big stops — including an outstanding glove save on Derek Roy's shot from the slot with just under 8 minutes left.
"That was a great move; the puck was kind of bouncing and he was able to get it between his legs," Smith said. "It was more luck than anything. I think it just ended up in my glove. But I'll take it."
By comparison, the 39 shots were a slow day at the office for Smith. He made a season-high 48 saves in a shootout win against San Jose on Nov. 2 and stopped 41 of 42 shots in a 3-1 win over the Los Angeles Kings on Oct. 29.
"I don't love it," Smith said of the heavy workload. "It's just the way things have worked out so far. Obviously, we want to tighten that up and get those shot totals down. Right now, we're just happy to get the two points."
His coach, Dave Tippett, was not entirely pleased with the Coyotes' performance.
"There were parts of that game I liked; other parts I really didn't like," Tippett said. "We didn't have enough players competing at the speed and level we needed to, but give our goalie credit. He played very well."
David Moss and Mikkel Boedker had the other Phoenix goals.
Maxim Lapierre and Polak scored for the Blues. Halak made 16 saves.
Alexander Steen had an assist to extend the longest active point streak in the NHL to 11 games. Steen, who has 10 goals and four assists during that stretch, has the longest scoring streak for a St. Louis player since Keith Tkachuk went 12 games in 2002-03.
"We worked, we competed and we created scoring chances," Blues coach Ken Hitchcock said. "We had some people that were really, as the game wore on, became major players in the game for us. But we didn't outwork the goalie."
The Blues trailed 2-1 going into the third period, but tied it at 2:49 when Steen found Polak sneaking in from the right point and hit him with a cross-ice pass. Polak beat Smith high with a shot from the circle.
Lapierre gave the Blues a 1-0 advantage when he tipped home Jay Bouwmeester's shot from the point 5:53 into the game. Moss tied it 2:56 later when he beat Halak with a wrist shot from the right circle.
With less than minute remaining in the first period, Blues defenseman Kevin Shattenkirk got caught pinching in, leading to a 3-on-1 break. Boedker took advantage when he converted a centering pass from Rob Klinkhammer with 31 seconds left in the period to give the Coyotes the lead.
NOTES: Phoenix's Martin Hanzal, who was tied for the team lead with 14 points, was a late scratch due to an undisclosed illness and is day to day. ... Steen played his 300th game with the Blues. ... Phoenix is 8-0-0 when leading after one period.