The Owls last won a bowl game in 1979 when they defeated Cal, 28-17, in the Garden State Bowl.
Chris Coyer ran for 70 yards and Matt Brown added 49 yards rushing and a touchdown for the Owls (9-4), who ran over 200 yards for the eighth straight game. They finished the contest with 253 yards on the ground.
Coyer also threw for 169 yards and a score, Rod Streater hauled in a 61-yard touchdown and Evan Rodriguez caught two balls for 52 yards.
Brett Smith threw for 127 yards with two touchdowns and three interceptions, and ran for 65 yards for the Cowboys (8-5), who defeated Fresno State 35-28 in double overtime in the 2009 New Mexico Bowl.