The Flyers were 1 for 4 in the shootout, getting their lone goal from Danny Briere.
Sergei Bobrovsky, redeeming himself after an awful start against Washington on Tuesday, played extremely well and made 30 saves.
The Flyers' power play was abysmal, managing a total of two shots on its three chances.
After former Flyer Arron Asham went to the penalty box for cross-checking early in the third period, it was the Penguins who had the best scoring opportunity. But Bobrovsky, following a Claude Giroux breakaway, stopped Max Talbot on a shorthanded breakaway with about 16 minutes left.
Bobrovsky was good but also fortunate. Pittsburgh clanged shots off iron in the first seven-plus minutes of the third period. With 2 minutes, 39 seconds left, he robbed James Neal from in close to keep the game tied.
The Flyers did not get a third-period shot until 6:31 remained. It was just their 16th shot of the night, and only a late third-period "flurry" enabled them to equal a season-low for shots - 20 in a 4-2 win in New Jersey on Jan. 6.
Pittsburgh dominated the overtime, spending most of it in the Flyers' end. Bobrovsky was tested several times, and made a big stop on Kris Letang's blast from the high slot with about 2:10 left.
The Flyers did not get any shots in the overtime, and they headed to a shootout for the fourth straight game. They lost to Atlanta, defeated Dallas, and lost to Washington.
If Bobrovsky needed a jolt of confidence, he received it after making an acrobatic left pad save - he stretched as far as he could and looked like an orange Gumby on skates - to stop Tyler Kennedy on a breakaway 3:08 into the game.
Bobrovsky, coming off a poor performance in which he was pulled after 21-plus minutes against Washington on Tuesday, was sharp as he stopped all 11 Penguins shots in the opening period.
The Flyers used a bizarre goal by Mike Richards to take a 1-0 lead with 4:42 remaining in the first.
James van Riemsdyk's left-wing pass bounced off Richards' skate and he then swatted it, ever so slowly, over goalie Marc-Andre Fleury's left shoulder.
"We're just trying to get as many pucks to the net and create some loose-scramble goals," Richards said.
The Penguins took advantage of a borderline goalie-interference penalty on winger Andreas Nodl to tie the score on a power-play goal 1:01 into the second period.
Kennedy, after taking a feed from Kunitz, scored the equalizer on a drive from the right circle.
Late in the first period, Nodl sped around defenseman Ben Lovejoy, who appeared to ride him into Fleury. Nodl was given a penalty, and he shook his head and skated to the box.
If not for Bobrovsky, Pittsburgh would have built a nice lead in the second period. The 22-year-old rookie made several difficult stops in the period - none better than his save on Alex Kovalev on a rebound off the boards while the Penguins were on a power play with 4:13 left in the stanza.
Bobrovsky also made a key stop on Neal and another on Kovalev that ignited "Bob" chants.
The Flyers had two good second-period chances, but Fleury stopped van Riemsdyk and Andrej Meszaros on close attempts. The Flyers were outshot, 20-15, as the teams were locked in a 1-1 tie heading into the third period.
Entering the night, the Flyers had won three of four games against the Penguins this season, scoring 3-2 decisions in each of their victories.
Contact staff writer Sam Carchidi at firstname.lastname@example.org. Follow him on Twitter at twitter.com/BroadStBull.