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.
There are similarities between the start of the Harbaugh-Meyer era with the Bo-Woody rivalry, but it's too soon to say it's a new Ten Year War.
A path to the College Football Playoff is not a simple one for the Tar Heels despite their 10-1 record.
Cary Chow and Adam Rittenberg react to the latest College Football Playoff rankings.
The Dan Le Batard Show reacts to Michigan coach Jim Harbaugh smashing a buckeye nut at the grave of former Wolverines coach Bo Schlembechler, in preparation for the rivalry matchup against Ohio State.
Alabama's Kirby Smart is a leading candidate for South Carolina's head coaching position, while Houston's Tom Herman is no longer in the mix to replace Steve Spurrier.
Even after the midseason firing of Steve Sarkisian and the drama that followed, USC can still land a pretty big fish: a trip to the Rose Bowl.