The seventh-seeded Lady Vols (20-13) used a 10-0 run to take control in the final minutes after trailing much of the game. No. 10 seed Green Bay (28-5) went 6:07 without scoring after taking a 49-48 lead with 6:11 to play.
Tennessee improved to 28-1 all-time in first-round NCAA play and advanced to Sunday’s second-round contest against the winner of the game between No. 2 seed Arizona State and No. 15 New Mexico State.
Mercedes Russell scored eight points and grabbed 13 rebounds for the Lady Vols.
Allie LeClaire scored 14 points, Kaili Lukan 12 and Jessica Lindstrom 11 for the Phoenix.
Green Bay, the Horizon League regular-season and tournament champion, led by as many as eight points in the first half and five in the second.
The bigger Lady Vols finally began to exert control inside and caught the Phoenix at 40 on Cooper’s driving layup with 1:50 left in the third quarter.
After that, there were nine lead changes in a 5½-minute span. Lukan’s layup gave Green Bay its final lead, 49-48, then the freshman Cooper sank a jumper with 5:50 to go to put the Lady Vols ahead for good 50-49.
It started the 10-0 run that iced the game for Tennessee. DeShields capped the surge with a pair of free throws that made it 58-49 with 21 seconds to play.
The Lady Vols, who finished tied for seventh in the Southeastern Conference and had their worst NCAA seed in school history, clinched their 40th consecutive 20-win season.
The smaller Phoenix outrebounded Tennessee 40-38 and had a 30-22 advantage in points in the paint. But Green Bay, which relies on long-range shooting for its strength, was just 3-for-17 on 3s. Tesha Buck was 0-for-11 from the field, 0-for-8 on 3-pointers.
The Phoenix were up 38-33 after Lindstrom sank two free throws with 5:11 left in the third quarter. But Cooper hit a 15-footer, then converted a three-point play and it was tied at 38 with 2:40 left.
There were four lead changes in the final 1:08 of the quarter with Mehryn Kraker’s inside basket with three seconds left giving Green Bay a 45-44 lead entering the final period.
Green Bay guards broke through for layups against the bigger Lady Vols early.
The Phoenix opened the second quarter with an 11-2 run to lead 24-16 on LeClaire’s short bank shot with 5:15 left in the half.
At one point, Green Bay had a 14-2 advantage in points in the paint, but Tennessee finally began to dominate the game inside.
Russell, Tennessee’s 6-foot-6 center, had a pair of rebound baskets and the Lady Vols finished the half with an 11-3 surge. Bashaara Graves’ 12-foot jumper with 20 seconds left tied the game at 27-27 at the break.