GLENDALE, Ariz. -- The St. Louis Blues were already on a roll when they arrived in Arizona, but the Coyotes never seem to slow the Blues down.

Alex Pietrangelo, Scottie Upshall and David Perron scored and Jake Allen made 31 saves for his fourth shutout this season as St. Louis beat Arizona 3-0 on Saturday at Gila River Arena.

It was the Blues' seventh victory in their last eight games, their ninth straight victory over the Coyotes and St. Louis has earned at least one point in 13 consecutive meetings with Arizona (12-0-1). St. Louis climbed past Nashville into third place in the Central Division after the Predators lost to the Carolina Hurricanes on Saturday.

"We had a good start," said coach Mike Yeo, whose team played its sixth game in nine days. "We've tried to manage the schedule the best we could and it's odd for us to not skate the day before game and then not have a morning skate, but it worked out good tonight."

The Blues improved to 14-7-0 under Yeo, who replaced Ken Hitchcock on Feb. 1. St. Louis recorded five shutouts since the change and goalie Jake Allen saw a simple reason.

"In the first period, I faced three shots," Allen said with mild amazement. "The difference is we're not making errors with pucks. We're getting pucks out even if it's just flipping it into the neutral zone. That makes a big difference in the NHL today."

Mike Smith made 38 saves for Arizona, but fell to 4-13-0 in his career against the Blues.

"Mike was excellent," said Coyotes coach Dave Tippett, whose team's five-game point streak ended. "We were so poor in the first period. It was maddening to say the least.

"Not everybody. We had some guys trying but the ability to get in a battle and wanting to get in a battle to allow you to play in the offensive zone or clear your own zone, there were just not enough guys that were engaged in that. When you don't do that, the whole game is whizzing by you."

Coyotes defenseman Anthony DeAngelo earned a five-minute major penalty for boarding and a game misconduct 1:56 into the game when he lost his stick and then ran Blues left winger Zach Sanford from behind. Sanford's face crashed into the boards and he left the game, returning in the second period.

St. Louis cashed in with three seconds remaining on that power play when Pietrangelo's high shot from the point eluded Smith even though Smith had a clean look at it and there was no deflection.

Ex-Coyote Upshall made it 2-0 at 2:52 of the second period on St. Louis' first shot of the period. Upshall gathered a loose puck in the high slot, wheeled toward the net and fired a shot through a screen and between Smith's pads for his ninth goal of the season.

Smith stopped Blues leading scorer Vladimir Tarasenko on a penalty shot late in the second period to keep the team close. Smith's positioning was so good that Tarasenko skated all the way to the side of the net before attempting a weak shot from the goal line that never made it to the net.

"I outwaited him I guess," Smith quipped.

Perron scored into an empty net during a Coyotes power play with 1:03 left.

NOTES: Saturday's game was the first of three meetings in 12 days. The teams had not faced each other this season before this stretch. ... Blues LW Dmitrij Jaskin (upper body) and C Jori Lehtera (upper body) missed their third and fifth straight games, respectively. Both are considered day-to-day. ... Blues LW Robby Fabbri (ACL) is out for the season. ... Coyotes RW Shane Doan missed the game with a lower-body injury suffered Thursday against the Detroit Red Wings. ... Coyotes D Kevin Connauton (upper body) and C Alexander Burmistrov (concussion) missed their eighth and ninth straight games. ... Of the Blues' 12 remaining games, only two -- home games against the Nashville Predators and Calgary Flames -- are against teams in playoff position. ... The Coyotes honored RW Radim Vrbata with a pregame ceremony after he played in his 1,000th NHL game March 9 vs. Ottawa.