Oklahoma has games left against Oklahoma State next Saturday and at TCU on Dec. 1. Any loss also would eliminate the Sooners from consideration for an at-large BCS bowl berth.
Oklahoma improved to 4-0 in road games this season. The Sooners also beat Texas at the Cotton Bowl in Dallas.
It marked the first time in 16 tries that Oklahoma overcame a fourth-quarter deficit to win dating to 2007. The win moved Stoops within 10 of Barry Switzer's school record of 157.
"They ended up making one more play than we did," Holgorsen said.
The teams combined for 1,440 yards. The 778 yards surrendered by Oklahoma were the most in school history, surpassing the 616 yards allowed in a loss to Baylor last year.
The Bowl Subdivision record for the most yards by a team in a loss is 791 set by Nevada in a 64-45 loss to San Jose State in 2001.
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 got 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 an inside slant for the go-ahead score.
Smith's desperation pass as time ran out fell incomplete just short of the end zone.