Andrew Fitzgerald added nine points for Oklahoma (4-1)
Both teams split two games earlier in the classic. Oklahoma beat Texas-El Paso 68-61, but lost to No. 17 Gonzaga 72-47. West Virginia topped Marist 87-44 and was defeated 63-60 by Davidson.
This was just the second time in Big 12 history that two league teams have met in a regular season, nonconference contest. The other occurred in 1996 when Texas played Nebraska.
After Browne hit two free throws to tie it, Buddy Hield had a basket, M'Baye made a pair of free throws and Hornbeak connected on a 3-pointer as Oklahoma grabbed a 69-62 lead with 4:20 remaining.
Steven Pledger and M'Baye both made two free throws that extended the Sooners' advantage to 75-66 with 1:38 to go.
Jabarie Hinds hit a 3-pointer and Staten had a layup to get West Virginia within 57-56 with 8 1/2 minutes left.
M'Baye had 10 points as Oklahoma took a 42-37 halftime advantage.
Pledger's four-point play put Oklahoma up 19-14 with 11 minutes left in the half. Tyler Neal ended a 9-0 run for the Sooners with a long-range jumper that made it 34-22.
Browne's 3-pointer got West Virginia within 40-35 with a minute to go in the half.
West Virginia senior forward Dominique Rutledge had two points and four rebounds in his season debut.