The Bulldogs (8-14, 2-3), who led 54-44 with 6:38 remaining, clung to a 59-57 advantage at the 1:35 mark. On their next possession, Morgan, who had missed his first nine shots, hit a 3-pointer to give Yale a 62-57 cushion.
Morgan also made 4 of 4 free throws in the final 38 seconds and Cotton made 2 of 2 to protect the lead as the Bulldogs beat the Quakers (4-17, 1-3) for just the second time in their last 16 visits to the Palestra.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.