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GLENDALE, Ariz. • Jaden Schwartz headed to the Blues’ bench at the end of what he thought would be his final shift, but with two goals on the night, the Blues wouldn’t allow him to take a seat.

“I was coming off and my teammates told me to stay on and try to get the hat trick, so that was pretty cool,” Schwartz said. “It ended up working out with two seconds left.”

Roofing a rebound past Arizona goalie Mike Smith, Schwartz capped off his first-career hat trick with 2.1 seconds remaining, finishing off the Blues’ 6-1 victory over the Coyotes at Gila River Arena.

On a night when the Blues had to endure the loss of forward Paul Stastny in the opening minute of the game, the power play went four for four and six players finished with at least two points. Goaltender Jake Allen made 24 saves for the victory in his first start since April 2013.

“We kept coming,” Blues coach Ken Hitchcock said. “It was a very physical first period and we knew it was going to be like that. I like the fact that we stayed with it right to the end. We kept coming and that’s the way we have to play. We’re a much better team when we don’t absorb ... when we initiate.”

The Blues will back on the ice Sunday, wrapping up their three-game road trip in Anaheim at 7 p.m. at the Honda Center.

They will be without Stastny, who was wearing a sling on his left arm after Saturday’s game.

Stastny was hit by Arizona’s Martin Hanzal along the boards and then was bumped again later in his shift. He headed to the locker room just 59 seconds into the game and didn’t return due to what the team labeled an “upper-body” injury.

“He’s not going to play (Sunday) and then we’ll just see,” Hitchcock said. “He took a hit there and he’s kind of day-to-day and then we’ll just see where we’re at.”

The Blues were forced to double-shift some forwards and log a little extra ice time in Stastny’s absence, but they more than managed.

The power play was perfect against an Arizona penalty-kill unit that was 10 for 10 entering the game.

David Backes scored one of the Blues’ four power-play goals, giving the Blues a 1-0 lead with 2:18 left in the first period. The puck went in off Backes’ skate, but stood after an official review.

The goal end the club’s scoring drought at 115:32.

The Blues blew a golden chance to extend their lead in the second period, but a 3-on-0 break, with only Smith standing in the way, ended in a missed shot.

Steve Ott and Backes were leading the rush, with Ryan Reaves alongside, and when Ott dished to Backes, his attempt sailed wide.

Hanzal, who was involved in Stastny’s earlier departure, left himself in the middle period with a leg injury.

The Coyotes tried to muster some offense without Hanzal, but on Mikkel Boedker’s bid for his sixth goal of the season, Allen stoned him.

“I felt good,” Allen said. “I felt good the last two weeks in practice, since training camp ended. I know that I have the ability to play; it’s just trying to be confident that I can play night in and night out.”

Midway through the game, Schwartz absorbed a high hit from Arizona’s Martin Erat. Kevin Shattenkirk responded by going after Erat, as both players drew roughing penalties. Schwartz appeared fine and would make the Coyotes pay later — three times actually.

But first, the Blues’ Alexander Steen pumped in his first goal of the season. He took a net-front pass from Backes and ripped a shot past Smith for a 2-0 lead.

The Blues went back on the power play and Vladimir Tarasenko went on the prowl in the offensive zone. A pass by Tarasenko went off a Coyotes’ player and onto the stick of Schwartz in front of the net.

Schwartz picked his spot on Smith, putting the Blues ahead 3-0 with his second goal of the season with 7:06 left in the second period.

“It was another one of those bounces, right on my tape,” Schwartz said. “I kind of waited and waited and thought I should shoot it. It ended up going on.”

Tarasenko’s assist gave him three in the game.

Schwartz scored his second goal of the game in the opening minute of the third period for a 4-0 lead. Jori Lehtera won the face-off to Schwartz, netting an assist for his first point in the NHL.

Arizona responded with a power-play goal by Lauri Korpikoski, breaking Allen’s shutout bid and ending the Blues’ streak of not allowing a goal at 119:41.

Hitchcock thought Allen played well.

“He was sound, solid,” he said.

Lehtera later added his first goal in the NHL for a 5-1 lead and then assisted on Schwartz’s third goal, completing the hat trick for the final score.

The Blues had six players Saturday with at least two points: Tarasenko, Schwartz, Backes, Steen, Lehtera and Shattenkirk.

BLUENOTES

The Blues recalled defenseman Petteri Lindbohm from their AHL affiliate on Saturday and he is expected to play Sunday against Anaheim. ... The team’s healthy scratches Saturday awere forwards Chris Porter, Magnus Paajarvi and Lindbohm.

Jeremy Rutherford is the lead Blues beat writer for the St. Louis Post-Dispatch.