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.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
Graduate transfer quarterback Davis Webb has officially joined California, giving the Golden Bears an experienced option to replace No. 1 overall NFL draft pick Jared Goff.
First-year football coach Dino Babers, hired by former Syracuse AD Mark Coyle, is on the committee that will search for Coyle's replacement.
Hugh Freeze has some major holes to fill on offense with the departures of Laremy Tunsil and Laquon Treadwell, but there is Chady Kelly and good depth.
After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.
The destination for Week 6 of the Big 12 Ultimate Road Trip is unanimous, as all three conference reporters would head to the Red River Rivalry.