Pittsburgh moved into a tie with Philadelphia for the lead in the Atlantic Division, one point in front of New Jersey.
The Islanders have lost six in a row and eight of their last nine. Mike Comrie had two goals for New York.
Comrie tied it at 10:47 mark of the third period with a power-play goal.
Letang then gave Pittsburgh the victory with 3:39 remaining. He grabbed a turnover in the Islanders' zone and wristed a shot over the right shoulder of Rick DiPietro.
New York has scored just eight goals during its six straight losses.
Notable deaths of 2014 [PHOTOS]