Parise and Gionta netted goals, and Martin Brodeur turned away Rene Bourque and Mikael Holmqvist to give the Devils their second straight shootout victory and send the Blackhawks to an eighth consecutive loss. Mike Rupp scored in regulation for the Devils, who have won three in a row for the first time this season and five of six despite scoring only 10 actual goals.
Tuomo Ruutu had the lone tally for the Blackhawks.
New Jersey took a 1-0 lead just 2:31 in with the benefit of a lucky carom. Johnny Oduya fired a shot down the left boards, and goalie Brian Boucher - anticipating the puck's arrival - went behind his net.
The puck never reached the goalie because it hit a spot on the corner boards and bounced right to Rupp for an easy goal into the empty net.
Boucher was almost victimized again on a similar play but managed to scramble back into position to knock aside Patrik Elias' shot that would have given the Devils a two-goal lead.
The Blackhawks got even at 8:55 when Ruutu fired a shot from above the left circle that glanced off Devils defenceman Colin White.
Chicago outshot New Jersey 10-8 in the scoreless second period as both teams had several good scoring chances. Parise and Elias missed from the slot for the Devils, and Radim Vrbata had two late power-play chances for the Blackhawks.
In the third, the Devils outshot the Blackhawks 9-4, but couldn't solve Boucher despite slot chances from Gionta and Travis Zajac.
Notes: The Blackhawks, who had six days off before playing the Devils, kicked off a stretch of three games in four nights. They host the St. Louis Blues on Friday and the Columbus Blue Jackets on Sunday. ... Devils D David Hale was sent to Lowell of the AHL on a conditioning assignment. Hale has not played this season while recovering from eye surgery. ... Blackhawks G Nikolai Khabibulin missed a sixth straight game with a broken finger. Chicago LW Martin Havlat missed his seventh consecutive due to an ankle sprain. ... The Devils for 0-for-8 on the power play. The Blackhawks failed on four attempts and have gone six games without a man-advantage goal.