Cousins also grabbed seven rebounds for the Sooners (18-6, 7-4 Big 12), who bested the Bears for the second time this season.
Buddy Hield drained five 3-pointers en route to 19 points and Cameron Clark supplied 16.
Baylor (14-9, 2-8) was led by Isaiah Austin with 21 points and six rebounds.
Brady Heslip added 12 points.
2014: The Year in Music [PHOTOS]