After tying it with two goals in the second, the Islanders took control by scoring four times in the third in the opener of a five-game, eight-day trip.
After Serge Betsen had gone close for Wasps, Northampton assumed control and several times went close to scoring, but a combination of solid Wasps defence and Saints errors kept them scoreless.
Duke extended its lead with another 7-0 burst, with freshman Rasheed Sulaimon scoring a pair of driving baskets before Cook's 3 that appeared to have Duke in control.