Hinkle was just 1 of 6 from 3-point range but hit 12 of 14 free throws for the Eagles (1-2), who shot 80 percent (20 of 25) from the foul line in the contest.
The Owls (1-3) shot just 57.1 percent (8 of 14) from the stripe.
The teams traded leads in the first half until, down 18-16 with 3:22 left before the break, American’s Hinkle connected on a pair of jumpers that started an 11-0 run into halftime.
American led the rest of the way and won despite being outscored by FAU 38-35 in the second half.
FAU got within 49-45 with 2:23 left to play, but Hinkle then hit a 3-pointer that sealed it.
Kore White led FAU with 13 points.