Brandon Conley scored 12, including four of nine unanswered points in overtime for a 71-62 lead.
The Golden Eagles hit 20 of 26 free throws (77 percent), while FIU made 12 of 18 (67 percent).
Trailing 29-22 at halftime, Oral Roberts (4-1) regained and extended the lead to 60-54 on Conley's layup with 2:03 left. Kimar Williams hit a 3 to make it a one-point game, 60-59, then made a free throw and a layup to tie it at 62 at the end of regulation.
Adrian Diaz, Cameron Smith and Jason Boswell each scored 14 for FIU (3-2), with Diaz grabbing 13 rebounds.