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.
A UCLA football player was suspended indefinitely Friday after he was arrested on suspicion of rape.
The tougher tests await down the road for No. 3 Baylor Bears, but coach Art Briles has seen enough of his Bears to know this is his best team.
A decision has been made that Randy Edsall will not be the football coach at Maryland next season, and discussions are taking place about how and when to separate, a source said Thursday night.
Appalachian State's board of trustees has approved a five-year contract for third-year football coach Scott Satterfield, who guided the Mountaineers through the transition from FCS to FBS.
Florida State running back Mario Pender has been released from the hospital but could be given a medical redshirt if he cannot return to the field this season.
The University of Wisconsin agreed to a 10-year deal with Under Armour on Friday worth a total of $96 million in cash and the retail value of products received.