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.
Celebrity Families of 2014 [PHOTOS]