Doug Weight scored for the Islanders and Joey MacDonald made 27 saves in filling in for longtime starter Rick DiPietro, who had only played in one preseason game while working his way back from surgery.
The only goal Brodeur gave up came on a deflection off a teammate. Other than that he was perfect, although he got help when Richard Park had shots in the first and second period hit off goalposts.
Brodeur's best save came late in the first period on a penalty shot by Kyle Okposo. The young forward stumbled slightly after skating into the Devils' zone, but he got off a rising shot to the top corner of the net that Brodeur deflected away with his glove.
The four-time Vezina winner stopped Jeff Tambellino and Jon Sim in close late in the second period and he stopped two bombs from the point by new Islanders defenseman Mark Streit early in the third period with New York holding a 4-on-3 skating advantage.
In the final minute, he stopped another point shot by Streit through traffic and then came up big on the rebound by Mike Comrie.
Elias provided the game winner 29 seconds into the second period on a bang-bang play in front of the net. Brian Gionta sent a pass across the crease that Elias nudged toward MacDonald while the two bumped. The rebound lay in the crease for a second and that's all Elias needed to find it and backhand it into the net.
The Islanders started off slowly but come in the final two periods for Gordon, the AHL coach of the year last season with Providence. He got the Islanders job after Ted Nolan left in a disagreement with general manager Garth Snow.
The Devils had the better of the play in the first period but the teams left the ice tied at 1 thanks to a couple of crazy bounces.
Weight, who was signed as a free agent in the offseason, got his first goal with the Islanders when his centering pass hit off the skate of Devils' defenseman Paul Martin and slid past Brodeur at 9:48.
Parise, who led the Devils with 32 goals last season, tied the game on a power play. MacDonald stopped Martin's shot from the point, but the rebound angled to the right circle and Parise deposited a backhander into a wide-open net.
Notes: Center Josh Bailey, the No. 1 pick overall in the NHL draft in June, was scratched by the Islanders. He left practice on Thursday after 10 minutes. The team did not say whether he was injured. ... The Devils were 2-5-1 against the Islanders last season. ... Finnish defender Anssi Salmela made his NHL debut with the Devils.