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.
SEC Network's Summer Tour stops by Baton Rouge to visit with Les Miles and the Tigers.
Three-time NFL MVP quarterback Brett Farve shares his stories of coaching high school football at the LSU Coaches Clinic.
SEC Network looks back at the highs and lows of Tigers' season.
Baylor has released five signees from its 17th-ranked recruiting class, including J.P. Urquidez, Kameron Martin, Donovan Duvernay and Patrick Hudson. Sources said the others was Parrish Cobb.
ESPN's Jared Shanker and Matt Fortuna join The Paul Finebaum Show to break down the Week One showdown between Ole Miss and Florida State.
Gary Shelton of the Saint Peters Blog joins The Paul Finebaum Show to discuss the renewed energy of Florida football programs.