Braden Holtby stopped all three New York attempts after making 35 saves in regulation and overtime.
The Capitals, who improved to 6-1-1 in their last eight outings, moved into a share of the lead with Winnipeg in the Southeast Division.
The one point earned by the Islanders inched them in front of both New Jersey and New York Rangers into seventh place in the Eastern Conference playoff race.
Evgeni Nabokov made 21 saves for the Islanders, who had won five of their previous six outings.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut