Nabokov was busiest in the third period, making seven saves while improving to 10-1-0 in his career against the Capitals, all with the San Jose Sharks.
John Tavares scored on a first-period power play and Parenteau made it 2-0 New York 6 minutes into the middle frame after Frans Nielsen picked up a Washington turnover and fed him in the right circle for a one-timer.
Parenteau added a third-period goal for the Islanders, who beat the Capitals for only the second time in 14 meetings.
Tomas Vokoun turned aside 25-of-28 shots as Washington saw its seven-game home winning streak snapped.
Celebrity Families of 2014 [PHOTOS]