Fleury stonewalled three Islanders power plays and turned aside all 10 shots he faced in the final period in recording his second whitewash of the season and 18th of his career.
Adams was on the doorstep in front of the net to collect the rebound of an Arron Asham shot, putting it under the pads of Kevin Poulin 8:35 into the third period to give Pittsburgh all the offense it would need.
The Pens raised their record to 31-15-4 with their fifth win in six games.
Poulin stopped 30-of-31 shots for the Islanders.
Celebrity Families of 2014 [PHOTOS]