Webb took two hard hits at the end of an 11-yard run. Linebacker Isaiah Bruce forced the fumble and recovered it at the West Virginia 1.
The Mountaineers then drove the length of the field, with Smith scoring on a 38-yard run.
After Texas Tech's Austin Stewart fumbled away the ensuing kickoff at the 17, West Virginia kicked a short field goal to head into the locker room tied at 13-13.
Texas Tech's Olaoluwa Falemi was flagged three times for pass interference, the final time on a pass that teammate Stewart intercepted at the Red Raiders' 1-yard line early in the third quarter. Three plays later, Trickett threw a 4-yard scoring pass to Sims.