Brian Bernardi added 18 points while Rokas Gustys scored a career-high 17 with 10 rebounds and Denton Koon added 10 points for Hofstra (8-4).
Sacred Heart (1-10), which has lost 10 straight games, was up 41-37 at the break and pushed its lead to 50-39 early in the second half.
Bernardi nailed two straight 3-pointers to give Hofstra a 70-66 lead with 5:12 to play. Green drove for a layup and made seven free throws down the stretch to seal the win. Sacred Heart was held to seven points in the final six minutes.
Cane Broome was 11 of 23 from the field, finishing with 25 points and eight rebounds for Sacred Heart.