West Virginia has failed to reach 100 yards rushing in its previous three games, so Holgorsen stuck Austin, a wide receiver, in the backfield.
"They just finally gave me the chance and I just took advantage of it," Austin said.
Austin broke the rushing mark of 337 yards set by Kay-Jay Harris against East Carolina in 2004. He also topped the Big 12 all-purpose yards mark of 375 set by Hollis Mitchell of Texas in 2000 against Kansas and the school record of 356 set by Garrett Ford against Pittsburgh in 1965.
Stoops called Austin's performance one of the best he's seen in the Big 12.
"He's right up there with anybody," Stoops said.
Geno Smith went 20 of 35 for 320 yards and four scores for the Mountaineers. He became the first quarterback to surpass 300 yards against the Sooners this season.
Oklahoma couldn't hang onto a 31-17 halftime lead. The teams combined for 31 points in the fourth quarter, including four touchdowns over the final seven minutes.
Austin's 54-yard run, plus a pair of Oklahoma penalties on the play, gave West Virginia the ball at the Oklahoma 8. Smith then lofted a ball that Bailey caught in the left corner of the end zone, and the Mountaineers had their first lead at 43-38 with 7:12 left.
Stills finished with 10 catches for 91 yards and four scores. His 7-yard TD grab with 4:10 left gave the lead back to the Sooners, only to have Bailey cap a three-play, 92-yard drive with a 40-yard TD grab with 2:53 left, his third of the quarter.
That was plenty of time for the Sooners, who took over at their 46 after Brennan Clay's long kickoff return.
Jones hit Justin Brown with a 36-yard pass. A 10-yarder to Brown put the ball at the West Virginia 14. On fourth-and-3 at the 5, Jones changed the play at the line and found Stills on a slant for the go-ahead score.
"Landry audibled out to for the touchdown and Kenny ran a great route," Stoops said. "He fought his way to the inside position and those are tough catches."
Smith's desperation pass as time ran out fell incomplete just short of the end zone.