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.
Jeff Goodman logs all the coaching changes following the 2015-16 college basketball season.
Indiana guard James Blackmon Jr., who averaged 15.8 points in 13 games before being injured last season, has withdrawn from the NBA draft.
Isaiah Briscoe has decided to withdraw from the NBA draft and will return to Kentucky for his sophomore season. Marcus Lee intends to transfer.