Brian Brown contributed 22 points, including the go-ahead jumper in the fourth OT, for VMI (13-9, 6-3 Big South), while Rodney Glasgow added 21 points and 12 rebounds, and QJ Peterson had 20 points.
Brown also hit the 3-pointer at the end of regulation that tied the game at 73 to force the first OT, while Covington hit a jumper at the end of the second OT to force the third extra period. Both shots fell just ahead of the buzzer in the longest Division I game of the season.
"Bless my guys. I just kept telling them to believe," said VMI coach Duggar Baucom. "Some of those overtimes, we were completely out of it. Miraculous things had to happen and they did. I am super proud of my guys."
Gardner-Webb (12-12, 5-4) trailed 35-32 at the break but kept the score close as neither team broke open a double-digit lead.
Tyrell Nelson led the Runnin' Bulldogs with career-high 24 points and 25 rebounds, while Jerome Hill had 15 points and 15 rebounds.
The Runnin' Bulldogs led 73-70 with 9 seconds left in regulation, but VMI tied it on Brown's 3-pointer that banked in at the buzzer.
Neither team scored in the first 4 minutes of OT. Peterson put VMI ahead with a jumper with 52 seconds left, but Hill responded with a jumper moments later to tie it up at 75. Peterson then missed a jumper with 5 seconds left, sending the game into its second extra period.
Gardner-Webb led by as many as four points in the second OT but VMI closed back in, tying it at 88 on Covington's jumper at the buzzer. The Runnin' Bulldogs again jumped out to an early lead in the next OT period before VMI again tied it up at the buzzer, this time with Tim Marshall layup that made it 97-97.
VMI opened the final OT by scoring seven unanswered points sparked by Brown's jumper followed by a 3-pointer and layup from Glasgow to build a lead it would protect down the stretch.
"I told the guys when we went to the fourth overtime that someone was watching out for us," Baucom said. "Tonight we had guys who hadn't been real visible and that came up and were extremely valuable."
The Keydets hit 43 of 89 from the field (48 percent), including 12 of 27 from 3-point range. Gardner-Webb struggled from the field, hitting only 36 percent, but sank 25 of 30 from the free-throw line to stay close.