The Skyhawks (0-4) made a charge coming out of halftime and had a 19-point deficit down to three points twice, the final time with 6:49 remaining. But FIU outscored UT Martin 12-8 the rest of the way with Draper scoring nine points.
Alex Anderson led the Skyhawks with 26 points with Kedar Edwards 15.
Ray Rodriguez added 10 points for the Panthers (3-1).
FIU took a 42-23 halftime lead behind 15 points from Diaz, who was 6 of 6 before the break. The Panthers had runs of 10-0 and 13-0 over the final 11 minutes in building their halftime lead.
The game was played at James Madison University as part of the Men Against Breast Cancer Classic.