The win was the Chippewas' seventh straight.
Brown rushed 4 yards for a touchdown, then caught a 29-yard scoring pass from LeFevour with 9:16 left in the first half to put Central Michigan (7-1, 5-0 Mid-American Conference) ahead 14-7.
Matt Norsic kicked a 40-yard field goal to bring Bowling Green (3-5, 2-2) within 14-10 at halftime.
After Andrew Aguila made a 38-yard field goal early in the third quarter, LeFevour threw a 9-yard touchdown pass to Bryan Anderson with 10:02 remaining.
LeFevour was also Central Michigan's leading rusher with 128 yards on 22 carries.
Tyler Sheehan was 35-for-55 passing for 341 yards with one touchdown and one interception for the Falcons, who were held to 20 yards rushing.
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.
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.