Fleury had 22 saves in the contest to improve the Penguins' season record to 8-1.
Steven Stamkos scored the only goal for the Lightning. Antero Niitymaki faced 33 shots in the loss.
Bill Guerin gave Pittsburgh a 1-0 lead on a power-play goal at 4:57 of the first period. The Penguins took a 2-0 lead into the locker room thanks to Gonchar's late goal.
Stamkos cut Pittsburgh's lead to 2-1 on a power-play goal at 6:18 of the second; however Pascal Dupuis scored two minutes later to make it 3-1 and Michael Rupp scored an insurance goal in the third period.
Boston schools pull out free condoms over wrapping complaints
Millions of Getty images now available for free via embed tool