Tennessee (28-5), the No. 2 seed in the Spokane Region, advances to a second-round game Monday with No. 10 seed Pittsburgh (20-11), which beat Chattanooga 51-40.
The Lady Vols had a much tougher time than expected against the 15th-seeded Broncos (22-11).
Tennessee was clinging to a 63-58 lead after Boise State's Camille Redmon made the front end of a one-and-one with 2:51 remaining. But Redmon missed her second free throw, and Tennessee's Ariel Massengale sank a 3-pointer 13 seconds later to spark a game-clinching 8-0 run.
Brooke Pahukoa scored 22 points for Boise State. She had 18 in the first half, when she shot 7 of 7. Deanna Weaver added 13 points and Shalen Shaw had 10.
Massengale scored 18 points for Tennessee, which outrebounded Boise State 46-28.
Graves, Massengale, Warlick post-game audio