Wilbert, who then completed a two-point conversion pass, drove the Owls (2-6, 1-4 Sun Belt Conference) 74 yards in nine plays after the Trojans (4-4, 3-3) went ahead 27-26 on Shawn Southward's 31-yard run with 1:49 remaining.
The victory ended a six-game skid for the Owls, who lost 37-34 in double overtime to South Alabama last week. It also ended their streak of 14 conference losses, dating to 2010.
FAU led 17-0, but Troy tied it after scoring two touchdowns in the final two minutes of the first half. The second was set up by an Owls fumble at their 29.
Mitch Anderson's 47-yard field goal broke the tie and Wilbert's third touchdown pass made it 26-17 with 3:49 left in the third quarter.