Ray Lawry ran 68 yards for a score and gained 201 yards on 23 carries for the Monarchs (6-6, 4-4 Conference USA).
Heinicke was 31 of 48 for 275 yards, with an interception and touchdown passes of 3 yards and 12 yards to Antonio Vaughan and 2 yards to Zach Pascal.
With the game tied at 28 late in the fourth quarter, Heinicke put together a 16-play, 57-yard drive to the FAU 11 and Ziffer kicked the field goal with 2 seconds to play.
Jacquez Johnson was 9 of 19 for 133 yards for FAU (3-9, 2-6), and gained 71 yards on 10 carries, including an 11-yard scoring run in the fourth quarter to tie it at 28. Tony Moore scored on a 1-yard run and Lucky Whitehead returned a punt 73 yards for a score.