After a scoreless first period, the Penguins were able to put five shots past Mike Smith in a mere 20 attempts.
Steven Stamkos reduced the Tampa Bay deficit to one 5:30 into the third period with his 15th goal of the season, but Maxime Talbot, Sidney Crosby and Deryk Engelland scored in a span of 6:38 to turn the game into a rout.
Crosby's goal was his 11th.
Tampa Bay has lost two in a row and five out of six. The Lightning learned earlier in the day that captain Vincent Lecavalier would miss at least three weeks with a non-displaced fracture in his right hand.