Brian Campbell and Marcel Goc also scored and Fleischmann added two assists for the Panthers. Scott Clemmensen stopped all 15 shots he faced in the third after replacing Jose Theodore during the second intermission. Theodore stopped 15 of 19 shots through the first and second period.
Kopecky, who has six goals in his last six games, scored his third of the game on an empty-netter from his own blue line that made the score 6-4 with one minute left.
Fleischmann put the Panthers in front 5-4 when his slap shot from the right circle rifled past Fleury at 3:29 of the third.
The Panthers, who came in with only one power play goal in their last 24 chances -- including 0 for 17 at home -- scored four goals with the man advantage.
Both teams combined for seven goals in the second period. Trailing 4-1 at the 8:54 mark, the Penguins scored three unanswered goals to tie it heading into the third.
They closed to 4-2 when Jeffrey's shot trickled through Theodore's legs at 9:51. Martin's goal, a slap shot from the right circle, pulled the Penguins to 4-3 at 14:08. Pittsburgh then tied it on a power-play goal by Kunitz with less than a minute left. His shot bounced off the skates of Florida's Mike Weaver and ricocheted back into the net.
Leading 2-1, the Panthers scored two goals in a 32-second span of the middle period -- both with the man advantage. Campbell's slap shot from the left circle beat Tomas Vokoun on the glove side at 8:22. Goc poked in a loose puck at 8:54, his first goal of the season, to make the score 4-1. Vokoun, who had 18 saves on 22 shots, was then replaced by Fleury.
The Panthers took a 2-1 lead on Kopecky's second goal. The Penguins had just killed a 5-on-3 power play when Kopecky found a loose puck in front and poked it past Vokoun at 3:22 of the second.
The Penguins tied it 1-all on Neal's goal. His shot from well above the top of the right circle got by Theodore 51 seconds into the second period.
The Panthers took a 1-0 lead in the first on a power-play goal by Kopecky. Campbell's shot from the top of the left circle was blocked by Vokoun but Kopecky grabbed the rebound and swept it in at 13:57.
Pittsburgh's Evgeni Malkin remains sidelined with a concussion suffered in Friday's 3-1 over the Panthers and didn't make the three-game road trip. ... Florida recalled C Scott Timmons from AHL San Antonio. ... C Stephen Weiss missed Tuesday's game while traveling to Toronto to attend his grandmother's funeral.
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SUNRISE, FL - FEBRUARY 26: Tomas Kopecky #82 of the Florida Panthers celebrates his goal with teammates against...
(Photo by Eliot J. Schechter/NHLI via Getty Images)