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.
Oregon State and former coach Mike Riley face a federal Title IX lawsuit filed by a woman who said she was raped as a result of the coach's failure to correct a sexually violent culture.
Los Angeles prosecutors have charged a man in connection with the theft of the University of Southern California's copy of O.J. Simpson's Heisman Trophy more than 20 years ago.
A months-old Facebook post has cost the Nebraska football stadium announcer his job one day after his hiring was announced.
Former running back Lawrence Phillips has been charged with first-degree murder in the April death of his cellmate at Kern Valley State Prison.
Michigan State quarterback and Heisman Trophy hopeful Connor Cook said he was disappointed his teammates didn't vote him among the team's three captains this season.
Michigan coach Jim Harbaugh said Tuesday he has informed competing quarterbacks Jake Rudock and Shane Morris of his decision on a starter for the Wolverines' opener Thursday night at Utah.