Jaden Schwartz completed his first NHL hat trick with 3 seconds to play, goalie Jake Allen was strong in his first NHL start in two seasons, and the St. Louis Blues dominated the Arizona Coyotes 6-1 on Saturday night.

St. Louis' Jori Lehtera scored his first career goal and had two assists.

David Backes and Alexander Steen each had a goal and an assist, and Vladimir Tarasenko assisted on three goals. Lauri Korpikoski ruined Allen's shutout bid with 9:32 left.

Backes' goal, Lehtera's goal, and Schwartz's first score came on power plays.

Schwartz, who also had an assist, made a shot from the point just before the game ended. Allen finished with 24 saves.

Beleaguered goalie Mike Smith had 30 saves for Arizona. Smith has allowed 15 goals in his three games.

Allen, the AHL's top goalie last season, made his first NHL start since April 21, 2013.

Both teams lost key players to injury.

St. Louis' Paul Stastny, who had four points in three games before Saturday, left with an upper-body injury early in the second period. He was holding his left wrist as he left the ice.

The Coyotes lost Martin Hanzal to a lower-body injury with 13:21 left in the second period. The Arizona center had to be helped from the ice.

Smith withstood a flurry of St. Louis shots before Arizona's Oliver Eckman-Larsson was called for interference, the game's first penalty, with 2:36 left in the first period. Eighteen seconds into the power play, the puck was free in front of the Coyotes' net when it glanced in off Backes' left skate.

After a video review, the goal was upheld, officials ruling that it was not a distinct kick as required to nullify the goal.

It was Backes' second goal of the young season and the first power-play goal allowed by Arizona. The Blues had a 15-7 advantage in shots in the first period.

Backes had another great chance at a goal in the second period when St. Louis had a 3-on-0 advantage, but his wide open shot missed the net far to the left.

No matter. St. Louis got two later in the period, on goals by Steen and Schwartz. Schwartz netted his second goal in the third period to make it 4-0.

NOTES: Arizona was 10-for-10 on penalty kills before the Blues' first-period, power-play goal. ... The Coyotes have allowed nine first-period goals in their first four games. ... St. Louis has won five straight in Arizona and nine of 11 against the Coyotes. ... St. Louis was 3-for-4 on power plays. ... Since 2008-09, Backes is the only NHL player with over 300 points and 1,300 hits. ... The Blues played at Los Angeles on Thursday before going to Arizona for Saturday's game. They will head back to Southern California to face the Anaheim Ducks on Sunday.