Keevan Lucas finished with 10 receptions for 193 yards and two touchdowns to help first-year Tulsa coach Philip Montgomery earn his first career victory.
After Greg Joseph's 27-yard field goal gave FAU a 44-41 lead following the first possession of overtime, Langer finished the game with four-straight carries, including a 3-yard touchdown run.
Tulsa's Dane Evans completed 21 of 33 passes for 424 yards and two touchdowns.
Joseph hit a career-long 47-yard field goal to give FAU a 41-38 lead with 1:48 left in regulation, but Redford Jones' 39-yard field goal with 3 seconds left capped a 12-play, 53-yard drive by the Golden Hurricane and forced overtime.
FAU's Greg Howell rushed for 138 yards and two touchdowns.