Not expected to be a factor in the Big East this season, the surprising Cardinals (5-4, 3-1) won their third straight in a tight race and dealt a severe blow to West Virginia's title chances.
Louisville also got a payback of sorts after being overlooked in the recent Big 12 expansion sweepstakes, a bid that went to the Mountaineers.
Geno Smith threw for 410 yards and three scores but couldn't bring the Mountaineers (6-3, 2-2) back from 10 points down in the fourth quarter.
Despite being out-gained 533-351, Louisville converted all four scoring chances inside the 20-yard line after failing on half its attempts all season.
Tyler Bitancurt missed one field goal try and had another short one blocked by Adrian Bushell on the first play of the fourth quarter. Johnson picked up the loose ball and went 82 yards to put the Cardinals ahead 31-21.
Smith, who completed 31 of 44 passes but was sacked three times, fumbled the ball away on the next series near midfield. He made up for it on the ensuing 96-yard drive with a 46-yard pass to Ivan McCartney that set up Shawne Alston's 8-yard scoring run with 9 minutes left.
But Louisville ran seven minutes off the clock on a 76-yard drive that included Dominique Brown's 2-yard run on fourth-and-1 at the West Virginia 43. Brown capped the drive with a 3-yard TD run for a 38-28 lead.
Stedman Bailey, who caught eight passes for 118 yards but had two critical drops, scored on a 1-yard pass from Smith with a minute left. But Louisville recovered the ensuing onside kick and ran out the clock.
Bridgewater, a freshman, completed 21 of 27 passes for a season-high 246 yards.
He provided a spark just before halftime after an 11-yard punt by West Virginia freshman Michael Molinari. Bridgewater went 5 of 6 on the drive, completing a left-handed shovel pass under pressure before hitting Eli Rogers from 4 yards out to tie the game at 21.
West Virginia went scoreless in the third quarter for the first time all season. Bitancurt missed a 33-yard field goal try after Najee Goode intercepted Bridgewater's first pass of the second half.
A fumble by freshman Andrew Buie at the West Virginia 15 set up Chris Philpott's 39-yard field goal to put Louisville ahead entering the fourth.