Kennedy's sixth goal of the season -- on the power play at 14:16 of the third period -- broke a 2-2 deadlock.
Goalie Dany Sabourin stopped 27 of 29 shots for the Penguins, who have won five of their last seven. They had lost two in a row by a combined 12-3 margin.
Rick DiPietro stopped 37 of 40 shots for the Islanders, who are the NHL's lowest-scoring team and haven't won two straight since Nov. 16-19, dropping 10 of 14 since that time.
On the power play, Pittsburgh went 1 for 6, and the Islanders were 1 for 2.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys