Trailing 2-0 after the first period, the Islanders evened it up with two second-period goals from Frans Nielsen (two assists) and Brian Rolston, then went up 3-2 on Matt Martin's goal 6:28 into the final period.
The Capitals forged a 3-3 tie when Brooks Laich scored on a power play midway through the frame.
But Parenteau then batted in the rebound of a Milan Jurcina shot for the decisive goal, also adding two assists en route to a three-point night as the Islanders broke a six-game losing streak.
Rick DiPietro turned aside 25-of-28 shots to earn the victory.
2014: The Year in Music [PHOTOS]