Nnemkadi Ogwumike added 16 points for Stanford (33-1), which will take on the fifth-seeded South Carolina Lady Gamecocks in the Sweet 16. Chiney Ogwumike scored 13 points and Toni Kokenis netted 10 points for the Cardinal.
Ayana Dunning paced the Mountaineers (24-10) with 13 points and nine rebounds. Asya Bussie scored 11 points and grabbed six rebounds for West Virginia.
Stanford took a 38-21 lead into halftime after it connected on 53.8 percent of its field goal attempts in the opening period. The Mountaineers shot only 26.7 percent from the floor in the first half.
The Cardinal cooled off after the break and made only 32.1 percent of their attempts from the floor, but managed to stay in front by converting 16-of-19 from the charity stripe in the final 20 minutes.
WVU shot 31.1 percent from the field in the contest. Stanford turned the ball over only six times and forced the Mountaineers into 13 turnovers.