ST. LOUIS -- The St. Louis Blues found a perfect cure for their recent woes -- a visit from the Arizona Coyotes.

St. Louis continued its domination over Arizona with a 4-1, come-from-behind win over the struggling Coyotes on Tuesday at Scottrade Center.

The Blues, winless in four of their previous five games, won their sixth successive contest against Arizona. They outscored the Coyotes 24-6 during the run.

In addition, the Blues have garnered at least one point in their last 10 contests with Arizona (9-0-1).

The Coyotes completed a five-game road trip with a fifth successive loss. They were outscored 24-10 during road swing.

The Blues managed just one goal per game in their previous three home contests, but they were able to snap back against their favorite opponent.

"I wasn't really too worried," St. Louis left winger Alexander Steen said. "We have a solid hockey team, mentally strong. We regrouped, and we grabbed it."

Steen and defenseman Kevin Shattenkirk led the way with a goal and assist each.

"Quite frankly, our best players were our best players," St. Louis coach Ken Hitchcock said. "It's all guys who have been through this before."

Steen helped turn the game around with the Blues' first short-handed goal of the season. The tally, which came with 8.8 seconds left in the second period, put the Blues ahead to stay 2-1.

"It did feel good," Steen said. "It was a good time in the game to get one. We'd been battling hard, and to get one like that was nice."

Shattenkirk set up the play by blocking a shot. He then jumped to his feet and started a two-on-one break.

"Luckily, the pass landed perfectly," Shattenkirk said. "The crazy thing was how well he waited on it and then was able to be patient and let it fall onto his stick."

St. Louis goaltender Jake Allen made 22 stops.

The Blues scored four unanswered goals after falling behind 1-0 in the first period.

Right winger Vladimir Tarasenko tied the game by converting off a perfect pass from left winger Magnus Paajarvi early in the second period. It was Tarasenko's team-high 16th goal and his eighth in his past eight home games.

Shattenkirk pumped the lead to 3-1 with his fourth goal of the season 6:53 into the final period. Center Jori Lehtera found Shattenkirk wide open on the play.

Center David Backes added an empty-net goal with 1:02 remaining.

Arizona bolted to a 1-0 lead on a goal by right winger Steve Downie 12:12 into the contest. Downie, stationed in front of the net, pounced on the rebound of a shot by right winger Brad Richardson.

The Coyotes gave up numerous odd-man rushes over the last two periods.

"If I knew (how to fix the issue), I'd do something about it," Arizona defenseman Oliver Ekman-Larsson said. "They had a lot of two-on-ones. I had to do a better job."

Arizona coach Dave Tippett also lamented the miscues.

"It's turnovers you see and turnovers that you don't see," Tippett said. "It's about capitalizing on them, and they did."

Arizona had the first eight shots on goal in the game and held the Blues without a shot until Shattenkirk's wrister was turned aside by Coyotes goalie Mike Smith with 6:26 left in the opening period.

Smith finished with 18 saves.

NOTES: St. Louis D Petteri Lindbohm, recalled from the Chicago Wolves on Sunday, made his season debut against the Coyotes. He finished plus-1. ... Arizona RW Shane Doan missed his eighth successive game with a lower-body injury. Doan has been skating and is listed as day-to-day. ...Arizona RW Viktor Tikhonov, claimed off waivers from the Chicago Blackhawks on Sunday, played on Tuesday. Tikhonov was drafted by Arizona in the first round of the 2008 draft and had eight goals and eight assists in 2008-09 with the Coyotes. ... St. Louis LW Steve Ott is out at least three months with a hamstring injury suffered in the first period of Saturday's 4-1 loss to Toronto. Ott missed six games Nov. 7-17 with an upper-body injury.