Terrell, who completed 15 of 20 passes, connected with Davis for a 33-yard score to give the Broncos (8-3-, 6-1 Mid-American Conference) a 22-17 lead in the last minute of the first half. Their 7-yard hookup, after Trevor Sweeney recovered Amari Coleman's fumbled punt at the Western Michigan 2, was the back-breaker with 5:47 remaining.
Cooper Rush's two touchdown passes in the first quarter gave the Chippewas (7-5, 5-3) a quick lead but Western Michigan scored 22 points in the second quarter.
Rush completed 24 of 44 passes for 248 yards but threw three interceptions.
Daniel Braverman had five catches for 117 yards for the Broncos with Davis finishing with nine receptions for 104.
Western Michigan last won six straight in 2008, 2000 for all MAC wins.