Claude Giroux added an empty-net goal to secure the Flyers' fifth third-period comeback win since Dec. 4.
Goalie Steve Mason made a key kick save on Mikkel Boedker's ticketed drive from the high slot, preserving the lead and helping to give the Flyers a 4-1 record on the Western portion of their six-game road trip, which ends Tuesday in New Jersey.
The Flyers, who killed a late delay-of-game penalty on Steve Downie, will practice Monday in Voorhees before heading to Newark.
Wayne Simmonds knocked in a rebound of Voracek's shot, knotting the score at 3-3 with 15:38 left. The power-play tally gave Simmonds eight goals in his last seven games.
Brayden Schenn, set up by Vinny Lecavalier, had trimmed the Flyers' deficit to 3-2 by scoring his 10th goal - and third in the last four games - with 2:45 remaining in the second period.
Phoenix scored a pair of goals in the first 2:54 of the second period, but Scott Hartnell cut the deficit to 2-1, taking a pass from Mark Streit and one-timing a right-circle shot past Mike Smith - just 17 seconds after Lauri Korpikoski's goal.
It gave Hartnell points in seven straight games. He scored the goal shortly after coach Craig Berube called a timeout.
"Chief was sick and tired of it," Hartnell said of the Flyers' ragged play.
Berube said he called the timeout because the Flyers were "playing soft. We weren't assertive."
They were after the timeout.
Just 31/2 minutes after Hartnell's goal, however, the Coyotes regained a two-goal lead as Mikkel Boedker took a stretch pass from Yandle and beat Mason on a breakaway. Thirty seconds earlier, Mason had robbed Boedker on a rebound attempt.
Midway through the second period, Jay Rosehill and the Coyotes' Paul Bissonnette were in a long fight that, based on the number of punches thrown, was one of the most entertaining of the season. When the even bout ended, Bissonnette clapped as he skated to the penalty box.
The Flyers were coming off a 2-1 loss in Colorado on Thursday.
"It's a mental challenge tonight, not thinking about getting home, thinking about getting two points tonight and putting yourself in a nice spot," Berube said before the game. "So it's important that mentally you're ready."
Phoenix was without injured defenseman Oliver Ekman-Larsson but was bolstered by the return of captain Shane Doan, who had missed the previous 12 games because of Rocky Mountain spotted fever.
"It's huge having him back," said Phoenix winger David Moss, whose team was 4-3-5 without Doan.