Bryzgalov, who already conquered his former team, 2-1, in Philadelphia on November 17, won his second straight start in his first appearance in the desert since losing Game 4 of a Western Conference quarterfinal series against Detroit last April.
"It's most important that we got two points," Bryzgalov said.
Matt Read picked up a goal and two assists in the early burst for the Flyers, who have won four of their last five. Wayne Simmonds, Claude Giroux and Scott Hartnell also lit the lamp in the opening 20 minutes.
"You play one game in a month and get thrown out there against a team like Philly when they're flying like that, it's not always easy," said LaBarbera. "But it's part of the job and you find a way to do it."
Read gave the Flyers a 1-0 lead on a power play just 4:23 into the contest as an errant Phoenix clearing attempt bounced off the dasher and into the slot for an easy one-timer.
Simmonds doubled the edge at 6:01 with his first goal in eight games, batting a loose puck out of the air, off Smith's pad and in from the left side of the crease.
It was 3-0 for Philadelphia with 3:47 to go in the first as Kimmo Timonen carried all the way around the Phoenix net from left to right before finding Giroux for a bullet from the right circle.
Hartnell then flipped in a Danny Briere pass from atop the crease for a 4-0 game on a power play at 18:29.
"We discussed starting better, especially (playing) on back-to-back nights. You know it's going to be tough to play from behind," said Briere.
Whitney ripped a bouncing shot by Bryzgalov on the short side at 7:15 of the second, and the Coyotes began to take control.
Yet their former goaltender turned them away, ending the period with a flashy glove save in traffic on a Whitney shot during a late power-play chance. Phoenix assumed a 13-6 edge in shots but still trailed by three.
A Keith Yandle prayer from the left point was answered by a Boedker deflection with 40.5 seconds remaining, but the Coyotes had nothing left in the tank.
Read became the first Philly rookie to record a three-point period since Joni Pitkanen did so on February 21, 2004 against Carolina...The Flyers have won six of 11 games in Phoenix since the Jets franchise relocated there in 1996...This was just the second win for Philadelphia in Arizona since March of 2000...The Coyotes had won five of the six previous home meetings...The Flyers improved to 9-3-1 on the road this season.