Brown's trey -- his first since Dec. 17 -- came off an assist from Marcus Smart and boosted the Cowboys (14-2, 2-1 Big 12) to a second straight win after a road loss to Kansas State.
Brown finished with 12 points and seven rebounds while Smart provided 22 points with a career-high 13 rebounds.
Le'Bryan Nash added 18 points.
The Mountaineers (10-6, 2-1) got 21 points from Terry Henderson and 20 from Juwan Staten.
Devin Henderson recorded 12 points and 13 rebounds.