After Phillip Carr's 3-pointer made it 61-57 for Morgan State (2-5), Wagner (3-2) outscored the Bears 5-0 in the last two minutes.
Dwaun Anderson sank two free throws and Michael Carey made a layup to tie at 61-61 with just under a minute left. In the final minute, Carr missed a 3-pointer and, after Saunders' go-ahead free throw, Clive Vaughan rebounded the missed second foul shot but missed a 3-pointer at the buzzer.
Saunders finished with 9 points for Wagner, Corey Henson led with 17 and Anderson scored 13. Carey scored 9 points and grabbed 10 rebounds.
Carr scored 17 points for Morgan State on 5-for-9 shooting with two treys and eight boards. Vaughan and Kyle Thomas scored 12 points each.