Dunn was 6 of 14 from the field, but hit all nine of his free throws.
Providence led by double figures for most of the second half. Rob Ukawuba's 3-pointer with 3:18 left pulled NJIT to 70-65, but Dunn answered with a 3-point play. Ben Bentil and Dunn combined to make 8 of 8 free throws in the final 2:30.
Rodney Bullock added 16 points and 12 rebounds for Providence (4-0). Bentil finished with 21 points.
Bullock's 3-pointer with 4:21 left in the first half gave Providence a 33-18 lead, but the Friars scored just four points the rest of the way for a 37-27 halftime advantage.
Damon Lynn led NJIT (3-2) with 24 points and Ukawuba 20. The Highlanders made 9 of 21 3-pointers but turned it over 22 times.