Fleury stopped Matt Read's shot from the corner, but Voracek pounced on the rebound to cap a furious rally from a 3-0 deficit. Daniel Briere scored twice, and Brayden Schenn added a goal in his playoff debut. Ilya Brzygalov settled down after a shaky start to finish with 25 saves.
Sidney Crosby, Tyler Kennedy and Pascal Dupuis scored for the Penguins, and Marc-Andre Fleury stopped 22 shots, but Pittsburgh struggled after dominating the first period.
Game 2 is Friday night in Pittsburgh.
The rivals delivered on their promise to play "whistle-to-whistle" and leave out the rough stuff that highlighted their six regular-season meetings. The game featured only a handful of penalties and little of the typical animosity.
Crosby missed the playoffs last season while dealing with concussion-like symptoms and the memory of watching from the rafters as the Penguins lost to Tampa Bay in seven games remains fresh.
The former MVP wasted little time making up for lost time. He gave Pittsburgh the lead on his second shift, shaking off a hit Philadelphia defenseman Braydon Coburn in the corner then bouncing to his feet and flipping a rebound over Bryzgalov's glove 3:43 into the first period.
Kennedy made it 2-0 just over 4 minutes later, his wrist shot from the left circle beating Bryzgalov over his stick.
Philadelphia coach Peter Laviolette called timeout, a maneuver he used successfully 10 days ago after the Flyers fell behind by two goals in the first 5 minutes. It worked April 1, as Philadelphia rallied for a 6-4 victory.
It worked. Just not immediately.
Dupuis gave Pittsburgh a 3-0 advantage with just 37 seconds left before the first intermission, scraping a puck off Bryzgalov's pads and into the net. The goaltender appeared to have no clue where the puck was on the play.
The Flyers limped to the dressing room but - as they have all season - they rallied.
Philadelphia won 20 games during the season when the opponent scored first, the most in the NHL. The Flyers showcased that resiliency during the final two periods of regulation, clamping down on Crosby and NHL-leading scorer Evgeni Malkin.
Briere gave the Flyers life with a breakaway goal 6:22 into the second period, even though replays showed he was well offside on the play. He brought Philadelphia within a goal with 10:37 left in regulation with a wrist shot from a tough angle that clanged off the far post and in.
Schenn tied it just over 3 minutes later by redirecting a shot by Scott Hartnell and setting up the kind of taut finish expected in perhaps the most competitive first-round series of the playoffs.
NOTES: The Flyers are 3-1 in overtime in Pittsburgh ... The Penguins scratched D Matt Niskanen, who missed the final two games of the regular season with an upper-body injury ... The Penguins are 6-2 in series in which they have home-ice advantage during Crosby's career ... Philadelphia D Marc-Andre Bourdon left the game with an upper-body injury and is day-to-day.