LMU's Marin Mornar missed a 3-pointer hard off the glass in the final seconds. Godwin Okonji quickly followed with a putback but completely missed the rim and Payne was there to redirect it in off the glass.
Kruize Pinkins made 1 of 2 free throws to put USF up by one with 20.1 seconds left.
The Lions trailed 47-30 early in the second half, but David Humphries' jumper gave LMU its first lead at 65-63 with 3:35 left.
Ayodeji Egbeyemi had 19 points while Payne and Humphries added 13 apiece for the Lions.
Tollefsen and Pinkins both scored 19 for the Dons and Tim Derksen added 15.