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.