The Lady Tigers (28-7) trailed 35-24 with 12 minutes to play, but went on a 12-0 run over the next five minutes to get back into the game.
Fowles, who made 9-of-10 field goals, scored 14 of her team's 28 second-half points including a short jumper with 5:32 to play that put the Lady Tigers ahead for good, 40-39.
LSU will face 10th-seeded Florida State (24-9) on Saturday at the SaveMart Center in Fresno, Calif. Game times will be determined on Tuesday. The Seminoles defeated No. 2-seed Stanford late Monday in Palo Alto, 68-61, to advance to its first Sweet 16.
The Lady Tigers hold a 3-2 all-time advantage over Florida State, with LSU winning the most recent meeting on Dec. 27, 2003, at the Russell Athletic Shootout in Atlanta, 75-68. The other four meetings came between 1989-1992, each in the respective teams' early season home tournaments.
LSU finished 19-of-44 shooting (43 percent), making only 4-of-16 three-pointers and 7-of-13 free throws. The Lady Tigers committed 15 turnovers.
West Virginia (21-11), which lost its season-opener to LSU in Baton Rouge by 39, didn't score in the final 2:38. They shot only 38 percent from the field (18-48) including 1-of-12 from three-point range.
Ashley Powell led the Mountaineers with 13 points on 6-of-13 shooting, but committed five of their 14 turnovers. Chakhia Cole scored 11 points and grabbed five rebounds.
Fowles, who was frustrated early with three and four players surrounding her, broke out of her funk during LSU's big second-half run. She finished with 13 rebounds for her 61st career double double. She also blocked two shots.
After building a 16-6 lead in the first 10 minutes, LSU looked to be on its way to another blowout victory. However, West Virginia packed into a 2-3 zone that LSU wasn't able to again shoot its way out of.
The Lady Tigers cold shooting from the perimeter allowed the Mountaineers to creep back into the game late in the first half and cut the LSU lead to 21-18 at the half.
LSU shot only 36 percent in the first 20 minutes, and it only got worse to start the second half.
LSU missed 9-of-10 shots over nearly 12 minutes of game time and committed five turnovers, allowing West Virginia to not only take the lead but extend it to 35-24 with just more than 12 minutes to play.
Seeing its season flash before its eyes after allowing a 22-3 run, LSU came out of a timeout and responded offensively.
With leading scorer Olayinka Sanni on the bench after picking up her fourth foul with 15:19 left, Fowles went to work in the post. The 6-6 center scored six points in a 12-0 LSU run that gave the Lady Tigers a 36-35 lead.
With less than four mintues to play, LSU held a 42-39 lead when Sanni returned.
Still leading by one with under two minutes left, LeBlanc found Fowles open in the paint for an easy layup and a 46-43 lead.
LSU was able to stop West Virginia on its next possession and made 3-of-4 free throws down the stretch to save the victory.
For the second time in history of program, the Lady Tigers scored under 50 points and won. The other time was earlier this season at South Carolina (49-46 on Feb. 4, 2007).