The Big Red (6-8) never trailed and led by as many as 17 points in the first half and 22 in the second.
The Bearcats (2-11), who lost their seventh in a row, still trailed 76-65 with 4:54 remaining. They cut the deficit to 76-72 with 1:25 left, but Chemerinski's offensive rebound and layup made it 78-72 at the 0:55 mark.
Reed quickly answered with a 3-pointer to make it 78-75, but Galal Cancer made 1 of 2 free throws with 8 seconds left for Cornell.
Reed finished with 23 points and 14 rebounds for Binghamton, which shot 69.6 percent (16 of 23) in the second half. Rayner Moquete added 19 points.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.