The Dukes (1-1) closed the first half on a 22-13 run to take a 10-point lead into the break.
Northern Illinois (0-2) pulled back to within two early in the second half and trailed 53-51 with 3:58 remaining after a pair of Aaron Armstead free throws.
Andrey Semenov and Cooke each hit layups to put James Madison up by six. The Huskies responded as Travon Baker made two free throws and Askel Bolin hit a layup to pull back within two with 1:26 to play.
Semenov netted another layup and Curry made a late free throw to push the lead to five. Northern Illinois couldn't connect on its last 3-point attempts in the final 28 seconds of play.
Baker finished with 17 points and Armstead added 16.