GLENDALE, Ariz. -- Every time Jaden Schwartz got himself in front of the Arizona Coyotes net Saturday at Gila River Arena, a St. Louis Blues teammate seemed to find a way to get him the puck, and the Coyotes were unable to stop him.
Schwartz capped off his first NHL hat trick and a four-point night with a power-play goal with 2.1 seconds left in the Blues' 6-1 win against the Coyotes.
"It was one of those nights when I was in the slot and the puck kept finding me," said Schwartz, 22, who leads the Blues with seven points through four games. "Everyone has a game like that once in a while, and tonight was one for me.
"It didn't think I was going to get the last one. My teammates told me to stay on the ice and try to get it. I've never had a hat trick before, so it's pretty special."
There was little doubt on Schwartz's first two goals. Schwartz beat Coyotes goalie Mike Smith over the glove from point-blank range on each, helping to turn what was a 1-0 game after one period into a rout.
"Jaden's playing better and better. He has a lot of tenacity and a great shot," St. Louis coach Ken Hitchcock said. "I was really happy for him that he got the third goal; it's good for his confidence."
Vladimir Tarasenko assisted on each of the Blues' first three goals, Jori Lehtera had a goal and two assists, and David Backes and Alex Steen each had a goal and an assist for St. Louis, which has won five straight games in Arizona.
"We stayed with it right to the end. We kept coming, and that's the way we have to play," Hitchcock said. "We're a much better team when we don't absorb; we initiated. I thought we kept initiating the whole game."
Goalie Jake Allen, playing in his first NHL game in 18 months, made 24 saves and came within 9:32 of earning the second Blues shutout in three nights. Brian Elliott didn't allow a goal to the Los Angeles Kings in a 1-0 shootout loss Thursday.
Allen, who shut out Arizona in his only other start against the Coyotes, was named to the NHL All-Rookie Team in 2012-13 when he went 9-4-0 with a .905 save percentage and 2.46 goals-against average. He spent all last season with the Peoria Rivermen of the American Hockey League.
"He was sound and solid," Hitchcock said. "We've had really good goaltending in every game we've played this year, and that's a really good sign."
The win may prove costly for the Blues, who lost center Paul Stastny to an upper-body injury on his first shift. Stastny was hit on separate plays by Martin Hanzal and Mikkel Boedker and skated to the dressing room holding his left hand less than a minute into the game.
Hitchcock said Stastny is day-to-day and will miss the game at the Anaheim Ducks on Sunday.
Hanzal was helped off the ice with an apparent lower-body injury in the second period after he was hooked down in front of the St. Louis goal by Blues forward Patrik Berglund. Arizona coach Dave Tippett said Hanzal will be evaluated further Sunday.
Smith allowed six goals on 36 shots to continue his tough start to the season. He has allowed 16 goals in three starts.
But Smith wasn't the only Arizona player who struggled against St. Louis. The Coyotes were 10-for-10 on the penalty kill this season before allowing four power-play goals to the Blues, and they didn't offer much resistance.
"We just have too many players that are playing below what we need them to play," Tippett said. "You just go through the whole lineup here. This was a test against a real good team, and we didn't fare very well."
Lauri Korpikoski scored the Coyotes goal on the power play at 10:28 of the third period to spoil Allen's shutout bid.
"Hockey is a momentum game, and when one team gets it, you have to find a way to stop it," Korpikoski said. "Once they got the momentum, they held on to it and then a mistake ends of up in the net, we didn't find a way to push back."
Smith looked sharp early, making 14 saves in the first period. He stopped Tarasenko three times in the first 14 minutes, once on a point-blank chance off a behind-the-back pass from Schwartz. But St. Louis kept the pressure on, and when Oliver Ekman-Larsson was sent off for interfering with St. Louis defenseman Alex Pietrangelo, the Blues needed only 17 seconds to cash in.
Smith stopped Schwartz and Tarasenko in a wild scramble in front of the net before the puck went in off Backes' skate at 17:42 for his second goal. It was the ninth first-period goal the Coyotes have allowed through four games.
The Blues dominated the second period. After killing two Arizona power plays, Backes chased down a rebound behind the Coyotes net and fed an unmarked Steen inside the right circle. Steen beat Smith with a shot to the far post at 11:42, and the Blues were off and running.
Schwartz made it 3-0 on the power play 1:12 later. Arizona's Michael Stone failed to clear the zone twice before leaving Schwartz all alone to pop a Tarasenko feed past Smith.
Schwartz, who was credited with an assist on Backes' goal, made it 4-0 less than a minute into the third period on another point-blank chance, collecting a Lehtera faceoff win in the slot and shooting it by Smith.
After Korpikoski got Arizona on the board, Lehtera made it 5-1 when he beat Smith between the pads on the power play with 7:58 left in the game. Then Schwartz got his hat trick in the final seconds.