Joshua Phillips got off a 3-point jumper as time expired but came up short.
Georgia State (7-2), which has won four straight, was ahead 62-57 after Markus Crider's layup with :47 remaining. Middle Tennessee's Perrin Buford made two free throws and Darnell Harris nailed a 3-pointer to tie at 62 with :14 left.
Kevin Ware led the Panthers with 18 points. Williams was 9 of 12 from the line and had 13 points with five assists. Crider chipped in 12 points.
The Panthers hit a scorching 13 of 22 (59 percent) from the floor in the second half while limiting Middle Tennessee to just 8-of-26 shooting (31 percent) in that period.
Reggie Upshaw had 18 points and grabbed 10 rebounds for Middle Tennessee (7-3). Harris also had 18 points.