The victory was the first in an NCAA tournament for the Aggies (20-16), who won last weekend's Mid-Eastern Athletic Conference tournament.
NC A&T will now meet no. 1 seed Louisville Thursday at 6:50 p.m. in Lexington, Kentucky.
Underwood was nearly perfect for the game, hitting all six of his field goals, including both three-point tries, and missing just of six free throws.
Despite Underwood's heroics, the surprising Big South champion Flames (15-21), just the second team to make the tournament with 20 losses, almost won it at the end.
After Lamont Middleton missed the front end of a 1-and-1, John Caleb Sanders raced end to end and flipped up a left-handed layup in heavy traffic that momentarily stopped Aggie hearts. The shot refused to fall, however, and the Aggies' Jean Louisme grabbed the rebound with two seconds left to secure the victory.
Bruce Beckford added 16 points for North Carolina A&T, while Middleton finished with 14 points.
The Aggies had a 40-33 lead at the half, but three-point plays by Liberty's Andrew Smith and Tavares Speakes and a layup from Davon Marshall cut that lead to 42-41.
The teams then traded baskets on a 10-10 binge. That's when the Aggies made their big push, with a 10-0 spurt capped by Adrian Powell's three-pointer with just under eight minutes to play.
The Flames refused to be doused, however, and, in keeping with the apparent 10-point theme, proceeded to outscore N.C. A&T 21-11, paced by 10 points from Sanders. That put Liberty back by a single point, 73-72, setting up the franctic final moments.
Marshall led Liberty with 22 points and Sanders added 21 in the loss.
While the Aggies hit more field goals, they let the Flames stay in the game on free throws. NC A&T made 11 of 19, while Liberty hit 16 of 18.
However, where North Carolina A&T got 22 points from its bench, mostly from Underwood, Liberty had just a single point from its non-starters.