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.
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.