Licata was 25 of 36 for 298 yards passing. Anthone Taylor ran for 115 yards and two touchdowns.
The Bulls took an early lead when Licata found Matt Weiser for a 41-yard touchdown on the game's first drive. Taylor took it in twice in the second quarter for a 21-0 Buffalo lead.
Dillon Buechel connected with Devin Rahming for Duquesne's first score late in the second quarter to trail 21-7 at the break.
In the second half, the Dukes took a 28-24 lead on a Randy Morris TD run and a pair of touchdown passes from Buechel to Chris King.
But Licata wasn't finished, finding Ron Willoughby for two touchdowns on back-to-back possessions in the fourth quarter for the Buffalo win.