Zach Norvell Jr. hit a 3-pointer with 51 seconds left to put Gonzaga up for good 67-64.
After the Zags tied the game and forced a Spartan turnover, Norvell took a pass on the left wing a drilled his second triple of the game.
ON the season, Gonzaga averages 84.5 points, 39.9 rebounds and 15.7 assists per game.
West region 4-seed Gonzaga entered Thursday's game against 13-seed UNCG having won its last nine NCAA tournament openers.
UNCG was 0-for-13 in the first half from 3-point range as Gonzaga took a 32-23 halftime lead.
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Francis Alonso and Demetrius Troy led the way for UNCG with 16 points apiece, but Alonso was called for an offensive foul just seconds after Norvell's key three pointer.
Demontrae Jefferson, a 5-foot-7 guard, had 25 points and eight rebounds to lift No. 16 seed Texas Southern (16-19), which became the first team with a losing record to win a tournament game.
During the last few minutes of the second half the two teams were tied. That's a formula for an upset, especially when UNC-Greensboro sophomore forward James Dickey (10 points) got going late.
UNC Greensboro almost pulled off the massive upset over last year's national runner-up Gonzaga, but fell short in a 68-64 defeat. But UNC Greensboro's shooting wasn't any better - they shot 41.8% from the floor, were just 3/22 from three, and shot 50% from the charity stripe.
NEXT UP: Gonzaga: Saturday against the victor of Ohio State-South Dakota State. (12.2), Rui Hachimura (11.3) and Silas Melson (9.5). UNC Greensboro vs Gonzaga tv channel is on TNT.