The Panthers were able to bounce back after being outscored 16-3 in their past three games.
"It was better tonight," Panthers coach Kevin Dineen said. "We've been riding a roller coaster and that's a bad way to do an 82-game season; good, bad, good, bad. We're looking for a little stability to it."
Fleischmann stretched Florida's lead to 5-3 at 6:27 of the third. His shot from the left circle was blocked by Zatkoff, but Fleischmann skated in and poked in the rebound.
Boyes' second goal came just as a power play ended with 34 seconds left to make it 6-3. Boyes has scored four goals in the past three games.
"It's about opportunities and when you get them, capitalize on them," Boyes said.
Florida scored two power-play goals in the second to take a 4-2 lead. Huberdeau poked in the puck from in front during a 5-on-3 at 7:08. Barkov followed 1:06 later when his shot bounced off Pittsburgh's Paul Martin and into the net. They were the first power-play goals against the Penguins this year.
"It was a big night for us, a big character win against a very good team," Versteeg said. "So we're excited about that."
The Penguins closed to 4-3 on Dupuis's goal. Dupuis took a drop pass from Sidney Crosby and beat Markstrom on the short side at 12:13 of the second.
"They got some momentum off those two power plays," Crosby said. "I still think we had a number of chances to get it tied at four. They found a way to get that fifth one in. We obviously didn't really generate a whole lot after that."
The Panthers took a 2-1 lead on Versteeg's goal at 9:10 of the first. The Penguins tied it 2-2 when Tanner Glass tried a wraparound but the puck bounced around in traffic, then Adams poked in the rebound at 16:49 of the first for his third goal of the season.
The Panthers scored first when Boyes got the puck in the right circle and beat Zatkoff on the glove side at 1:55 of the opening period.
"Obviously not the result I was looking for," Zatkoff said. "It felt good at the start and they just kept coming. I didn't make any big saves. I needed to make a big save there and didn't do it. I need to get better and make sure I'm ready for the next one."
Pittsburgh tied it at 1-all on Malkin's goal at 5:38 in the opening period. Beau Bennett intercepted a pass at the blue line and passed to Malkin in the left circle. His wrist shot went under Markstrom's blocker.
Pittsburgh lost its first road game after winning its first three games at home. ... Pittsburgh played its first of back-to-back games of the season. The Penguins play at Tampa Bay on Saturday night. ... Florida celebrated its 20th home opener on Friday, and played its first back-to-back set of the season. They lost at Tampa Bay 7-2 on Thursday. ... Florida had just one power-play goal in its first four games.
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SUNRISE, FL - OCTOBER 11: Sidney Crosby #87 of the Pittsburgh Penguins warms up prior to the game against the...