Texas (7-2, 6-0 Big 12) maintained sole possession of first place in the conference over No. 5 Baylor.
The Longhorns sent the game into overtime tied at 40-40 on Anthony Fera's fourth field goal of the game, a 24-yarder with 13 seconds left in regulation.
McCoy threw three TD passes after halftime, including the short toss to fullback Alex De La Torre on the Longhorns' overtime possession.
Mario Alford ran 20 yards on West Virginia's first play of overtime, but Millard, playing in place of the injured Clint Trickett, threw two straight incompletions before his soft pass ended up in Edmond's hands.