Playing the last 12 minutes with four fouls, Shanece McKiney had 13 points, seven rebounds and five blocks, while DaShawn Harden added 12 points for LSU (21-12), which advanced to the Sweet 16 for a second straight season - both times with a second-round upset on its home court.
Next up for LSU is a rematch with Louisville. The two teams played in the preseason WNIT and the Cardinals came away with a 21-point win.
Holding a seven-point lead 5:05 left, West Virginia was on the verge of winning the first second-round NCAA game in program history, but LSU went on a 16-2 run. Asya Bussie had 21 points and Bria Holmes 12 for West Virginia (30-5), which fell to 0-8 all time in second-round games.
LSU appeared to be on its heels when Bussie's free throw made it 63-56 and capped a stretch in which WVU scored 13 of 15 points at the foul line.
Ballard responded with runner, sparking a 6-0 run that pulled LSU back to 63-62 with 3:30 left.
A day earlier, West Virginia coach Mike Carey had said he liked his team's chances in a close game with four minutes left, because WVU had been so solid closing out games all year.
Not this time.
Bussie's transition layup with 3:02 to go was WVU's only basket during a more than five-minute span, and LSU went up 72-65 when Ballard's free throws capped the decisive run.
Despite being without senior guard Jeanne Kenney, who went to the locker room in the first half with concussion symptoms, LSU expanded a one-basket halftime lead to nine at 46-37 when Jasmine Rhodes hit a runner to cap a 9-2 run. Rhodes was a virtual non-factor in LSU's offense for much of the season, but responded to an increase in playing time caused in part by Kenney's absence.
Foul trouble began to haunt the Lady Tigers soon after, however. With 12 minutes left, LSU's two best front court players, Theresa Plaisance and McKiney, were on the bench with four fouls each.
That allowed WVU to exploit mismatches with its top interior players, Bussie and Holmes, who combined for 10 points during a 16-2 run that gave the Mountaineers a 57-50 lead.
McKiney returns with about nine minutes left and Plaisance returned with 6:40 to go. Plaisance finished with nine rebounds and eight points in 28 minutes, and LSU outrebounded WVU 55-40.
West Virginia also hurt itself with poor shooting, hitting 19 of 63 from the field (30.2 percent).
looked genuinely out of sorts to open the game, hitting only three of their first 20 shots and missing its first seven 3-point attempts.
The 6-foot-4 McKiney was a big reason for that, swatting away four shots in the paint in the first 5:24.
LSU led by as much as nine points early on when Plaisance scored inside to make it 17-9, but WVU seemed to settle down soon after, and used a 12-2 run, capped by Christal Caldwell's 3 and fast-break layup, that gave WVU a 27-24 lead.
West Virginia 26 points during the final 10:35 of the half, but LSU was able to regain the lead at 37-35 when Ballard hit a driving, off-balance floater in traffic seconds before halftime.