Kevin Weekes had 23 saves in picking up his fourth straight win.
The two goals gave Parise a career-high 34, two more than he had last season.
Radek Martinek and Kyle Okposo scored for New York. Islanders goalie Joey MacDonald was outstanding on a night New Jersey had 50 shots.
Parise, who has a habit of being in the right place at the right time, got the winner with 7:25 to play in the third period on a power play. Martin took a shot from the point and Parise put the big rebound into an empty net.
The goal game just seconds after Weekes stopped Richard Park and Sean Bergenheim in close on short-handed chances.
Langenbrunner iced the game with his 17th of the season on a setup by Parise.
The Devils rallied late in the first and second periods to tie it at 2 heading into the third period.
Langenbrunner tied the score with less than 4 minutes left in the middle session with a slap shot from the left circle. The power-play goal came 18 seconds after Islanders captain Bill Guerin was called for hooking.
Okposo had given New York a 2-1 lead with a spectacular power-play goal earlier in the period. The second-year forward stopped a clearing pass by Johnny Oduya at the point, skated in and around defenseman Bryce Salvador and then put his own rebound past Weekes for his 11th goal of the season.
The Islanders took a 1-0 less than 3 minutes after the opening faceoff when Blake Comeau made a cross-ice pass to Martinek in the right circle for a shot into an open net.
Parise tied it with 1:21 left in the opening period. Martin, who had the primary assist on Langenbrunner's goal, took a shot from the right point and Parise put the rebound home.
Notes: Jay Pandolfo returned to the lineup after being a healthy scratch for nine straight games. ... Islanders RW Trent Hunter was scratched because of a hip flexor. D Mark Streit missed his fourth straight game with an upper body injury. ... Linesman Pierre Champoux took a hard fall late in the second period but didn't miss any action. ... Islanders F Doug Weight left the game with a knee injury. He will be re-evaluated on Thursday.
