At a school that's seen three different quarterbacks reach 5,000 yards passing in a season -- including head coach Kliff Kingsbury -- and three others surpass 4,000 yards, those passers accomplished little as freshmen or redshirt freshmen.
Webb broke the school freshman single-game record of 422 yards set by Billy Joe Tolliver against TCU in 1985 and surpassed the 415 yards Webb had last week against Iowa State.
For the day, Webb completed 36 of 50 passes, including a pair of 10-yard scoring passes to tight end Jace Amaro.
"It's encouraging to have a young QB like that and have guys step up around him and make those plays," Kingsbury said. "It bodes well for the future."
Fellow Texas Tech freshman Baker Mayfield, who missed his second straight game with a twisted knee, had 413 and 367 yards in his first two games this season, respectively.
Kingsbury, who doesn't let freshmen talk to the media, said Webb's work ethic steadily improved after he wasn't chosen to start the season.
"The more reps he gets, the better he gets and the more confidence he gets," Kingsbury said.
Texas Tech's Ryan Bustin kicked three field goals and Kenny Williams had a pair of 1-yard touchdown runs, including the go-ahead score with 9:20 left in the game.
Dreamius Smith ran for two touchdowns for the Mountaineers (3-4, 1-3), who punted on four straight possessions in the second half to let Texas Tech take over.
Kingsbury got a win in his first head-to-head matchup as a coach against West Virginia's Dana Holgorsen.
"We refused to coach well enough to win the game," Holgorsen said. "And obviously that will get addressed.
Kingsbury was the Red Raiders' quarterback from 1999-02. Holgorsen was the team's wide receivers coach from 2000-04 and added offensive coordinator duties from 2005-07. Holgorsen is credited with helping Kingsbury join him on Kevin Sumlin's staff at Houston in 2008.
West Virginia quarterback Clint Trickett, starting his third straight game, continued to be plagued by accuracy troubles and a habit of floating the ball up for grabs downfield. His receivers bailed him out at times and he finished 27-of-43 for 254 yards.
Instead, West Virginia found success in its running game against the Big 12's top rush defense.
West Virginia found the end zone on its first two drives of the second half. Smith followed a block from Charles Sims and slipped through a crowd around left end on a 12-yard scoring run put the Mountaineers ahead 27-16 late in the third quarter.
But West Virginia generated little offense the rest of the game.
"The effort was fine," Holgorsen said. "The will to win was not there."
Trailing 27-23, Webb found Amaro for a 37-yard completion and Brad Marquez for 16 yards early in the fourth quarter to set up Williams' second straight short scoring run.
The outcome was still in doubt until Webb found Amaro with a 10-yard scoring pass with a minute left.
"He's always very composed at the line of scrimmage," Amaro said of Webb. "He's been able to drive down the field when we've really needed it and that really helps us have a lot of confidence in him."
Amaro, who also had a 10-yard TD catch in the first quarter, finished with nine catches for 136 yards -- his sixth straight game with at least eight receptions. He increased his league-leading catch total to 56. Marquez had eight catches for 112 yards.
Texas Tech jumped ahead 13-0 but lost two second-quarter fumbles that allowed the Mountaineers to tie it at halftime.
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.
Top 25 Overview
It was over when... Texas Tech scored 21 unanswered points in the second half, moving the team into first place in the Big 12 conference.
Gameball goes to... Davis Webb. Webb completed 36 of 50 passes for 462 yards and two touchdowns, surging Texas Tech past West Virginia.
Stat of the game... 400. Webb has become the first Texas Tech freshman to surpass 400 yards passing in each of his first two starts.