The Mountaineers shot 48 percent against the Longhorns and finished the first and second halves strongly en route to the win.
With the win, the Mountaineers now move on to likely face No. 1 seed Stanford unless the Cardinal is upset by No. 16 seed Hampton.
With the game tied at 18, West Virginia went on a decisive 12-0 run to end the first half to give the Mountaineers a 31-18 advantage at the break. They cruised to the win in the second half.
Despite foul trouble from junior center Ayana Dunning that kept her on the bench, West Virginia found other scoring threats like guard Taylor Palmer who had 18 points.
WVU junior center Asya Bussie finished with 12 points and six rebounds.
The Longhorns were held to just 27.5 percent shooting in the losing effort.
Texas cut the lead to just three with less than four minutes to play, but Palmer drained a three to extend the WVU lead. After an offensive foul called on the Longhorns, two free throws made it an eight-point game with under three minutes to play.
Sophomore Jess Harlee followed that with a steal and layup to make it an 11-point game and seal the victory for the Mountaineers. The shutdown defender finished with 10 points and 10 rebounds. It was her second-career double-double.