The touchdown with 10:53 left capped a six-play, 77-yard drive that took just over two minutes.
Licata was 21-of-33 passing for 285 yards and the score.
The Broncos (4-7, 2-5) committed three turnovers after Licata's TD pass, including two in Buffalo territory.
The Bulls (3-7, 2-4) jumped to a 17-0 advantage on rushing touchdowns by Branden Oliver and Devin Campbell and a 30-yard field goal by Patrick Clarke before Western Michigan scored 21 straight points on three Alex Carder TD passes -- 17- and 27-yarders to Eric Monette and an 8-yarder to Kendrick Roberts.
Two more Clarke field goals propelled Buffalo briefly back into the lead, 23-20, before Andrew Haldeman put the Broncos ahead with a 28-yard kick, setting up the Bison's winning drive.