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 two 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.
The win allowed West Virginia (8-1, 3-1 Big East) to remain on Connecticut's heels for a berth in the Bowl Championship Series with three games left, including a key matchup next week at Cincinnati.
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 consecutive season.
White ran 24 times for 147 yards and threw for 181 more in his third stellar game against the Cardinals in a row.
Brohm completed 27 of 46 passes for 345 yards, but he was intercepted twice and sacked four times.