Junior guard Josh Perkins had 16 points and the Bulldogs (31-4) extended the nation's longest winning streak to 15 games despite shooting just 42.4 percent from the field and missing 12 free throws, including three in the final 10 seconds before Norvell Jr. iced the game on a foul shot with 7.8 seconds left.
Junior guards Francis Alonso and Demetrius Troy had 16 points apiece for the Southern League regular-season and conference tournament champion Spartans (27-8), who were making their first NCAA appearance since 2001. The 13th-seeded team had won six in a row and 11 of 12.
The Bulldogs will face fifth-seeded Ohio State in Saturday's second round.
Gonzaga, which lost to North Carolina in the NCAA championship game last season, is 21-1 since a 72-70 loss at NCAA qualifier San Diego State on Dec. 21, although this one was never easy.
The Cougars trailed by nine at half before gradually closing the gap. Alonso's bank shot with 7:24 remaining cut the Gonzaga lead to 57-54, and senior forward Jordy Kuiper's jumper from the right baseline from an Alonso feed capped an 8-0 to made it 57-56.
Troy hit two jumpers and Perkins made a floater in the lane to tie it at 60 with 3:22 remaining. Troy hit another layup to tie it at 62 with three minutes remaining, and Kuiper's tip-in at 1:49 gave the Spartans a 64-62 lead before Perkins' jumper tied it at 64 with 51 seconds left.
After Norvell Jr.'s trey, Alonso was called for an offensive foul for pushing off on a screen, but sophomore forward Rui Hachimura missed two free throws and UNC Greensboro rebounded.
Senior forward Marvin Smith's potential game-tying 3-pointer was in-and-out with 7.8 seconds left, and Norvell Jr. made a free throw to ice the game.
Freshman forward Corey Kispert had eight points and Hacihumra had five rebounds for the Bulldogs, making their 20th consecutive NCAA appearance. Gonzaga and Kansas entered this season as the only teams to have won nine straight NCAA openers.
Sophomore forward James Dickey III had 10 points and 11 rebounds for UNC Greensboro, which missed its first 13 3-pointers and was 3-for-22 from distance.
--Field Level Media
NC-Greensboro | Gonzaga | |
Francis Alonso 16 | Scoring | Johnathan Williams 19 |
Francis Alonso 2 | Assists | Josh Perkins 2 |
James Dickey 11 | Rebounds | Johnathan Williams 13 |
Francis Alonso 3 | Free Throws Made | Zach Norvell Jr. 7 |
James Dickey 1 | Steals | Josh Perkins 2 |
Jordy Kuiper 1 | Blocks | Jeremy Jones 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
NC-Greensboro | 64 | 41.8 | 3-22 | 5-10 | 7 | 39 | 1 | 4 | 13 |
Gonzaga | 68 | 42.4 | 5-23 | 13-25 | 7 | 33 | 2 | 5 | 10 |