Fuller scored a season-high 19 points and Jones added 18 points as the Trojans (2-3) snapped a three-game losing streak.
With the game tied, Jones split a pair of free throws for a 63-62 USC lead. Jones later hit a short runner with 35 seconds left for the three-point cushion.
Coming out of a timeout, Morgan State (0-4) was struggling to get into its offense when Larry Bastfield threw an errant pass into traffic that was intercepted by Fuller.
Ameer Ali scored 17 points and Kevin Thompson added 15 for the Bears.