Pittsburgh scored the game's final four goals to win its third in a row.
Marc-Andre Fleury started in goal for the Penguins and gave up four goals on 14 shots during the first period.
Tomas Vokoun replaced Fleury and was perfect over the final two periods while Pittsburgh was putting together its rally.
The Penguins faced a 4-1 deficit heading into the second and by the time the middle period was over they had tied it up.
Just 18 seconds into the third period, however, Kunitz put a slap shot past Boucher for the game-winner. Kunitz also scored Pittsburgh's opening goal in the first period.