Kennedy struck 21 seconds after the Lightning had tied the score 2-2 on a power-play goal by Martin St. Louis, batting in a rebound of a shot from the point by Brook Orpik that was touched in front of the net by Kris Letang.
Letang ended with two assists while Max Talbot and Arron Asham also scored for the Penguins, who improved to 10-1 in their last 11 post-season Game 3's.
Marc-Andre Fleury turned aside 25-of-27 shots, allowing only a pair of power-play tallies to the Bolts' St. Louis.
Dwayne Roloson made 27 saves for the Lightning, who will seek to even the series in Game 4 Wednesday in Tampa.
2014: The Year in Music [PHOTOS]