Ottawa scored in all three rounds of the shootout, also getting goals from Alexei Kovalev and Mike Fisher. The Islanders kept pace in the opening two shootout rounds but John Tavares was stopped by Pascal Leclaire to end the game.
Jon Sim produced the last goal in regulation, tying it for the Islanders with a wraparound shot just 56 seconds into the third.
Leclaire made 25 saves to get the victory, his 11th of the season.
The Islanders did not give up a power play goal and have killed off 13 consecutive penalties.