Davis went 17-for-33 through the air for 279 yards while Tracy Lampley hauled down six passes for 125 yards and two touchdowns as the Golden Eagles (11-2, 6-2 C-USA) collected their first conference title.
The Southern Miss quarterback also posed a ground threat, rushing for 71 yards on the ground on 14 carries, while on defense the Golden Eagles ran back an interception and a blocked punt for touchdowns.
The Cougars (12-1, 8-0) tasted defeat for the first time this season, costing them a bid to a BCS bowl game.
Case Keenum completed 41-of-67 passes for 373 yards and Michael Hayes rushed 15 times for 50 yards and two touchdowns for Houston.
2014: The Year in Music [PHOTOS]