It was the third shutout of the season for Fleury, tying him for the NHL lead, and the 26th of his decade-long career.
Kunitz opened the scoring 6:53 into the game and Fleury protected the one-goal lead until Brandon Sutter tallied on the power play midway through the third. Kunitz tacked on an empty-net goal with 1:43 to play.
Sidney Crosby assisted on all three goals, increasing his league-leading points total to 36. He has 701 points for his career.
Ben Bishop took the loss while making 28 saves.