Senior Anthony Drmic was held scoreless for the first time since his freshman year but grabbed nine rebounds for Boise State.
Leading by two at halftime, the Broncos extended their lead to 42-34 after an 11-2 run, but the Aggies closed to within 47-46 on Julion Pearre's 3 at 13:28. Hutchison had two dunks amid an 18-4 run and Boise State led 70-55 after Thompson's crossover and finish with 3:25 left.
Jalen Moore scored 18 points for the Aggies (9-5, 1-2).
After seven lead changes, Boise State pulled ahead for good, 28-25, on Thompson's three free throws.