Brian Brohm brought Louisville from 17 points down in the second half, with the Cardinals tying it on Art Carmody's 37-yard field goal with 3:05 left. White, who had threw TD passes, then capped a 65-yard drive with his scoring run up the left sideline.
Brohm, who broke his own Big East record with his seventh 300-yard game of the season, threw a desperation pass that Antonio Lewis intercepted at the West Virginia 7.
Louisville (5-5, 2-3 Big East) was eliminated from the conference title chase. The Cardinals need a win either at South Florida or at home against Rutgers to become bowl eligible for a 10th straight season.
Brohm completed 27 of 46 passes for 345 yards.