Kovalchuk went first in the shootout and beat Jose Theodore. Martin Brodeur responded by making stops on the Panthers' Tomas Fleischmann and Kris Versteeg and Elias then iced it with a shot that went between Theodore's pads.
Elias and Zach Parise scored in regulation time, and Kovalchuk had two assists for the Devils, who won for the fourth time in five contests.
Brodeur made 24 saves to notch the victory.
Versteeg got both regulation goals and Theodore made 32 saves for the Panthers.