It was the first triple-double at BYU since 1988.
The Cougars (7-2) made 18 of 21 free throws in the second half and shot 58 percent after taking a 37-30 lead at the break.
BYU finished 23 of 27 from the line and outrebounded Hawaii 48-30. Chase Fischer contributed 20 points.
Hawaii was within 54-50 after a Bobbitt basket at the 11:04 mark but Fisher hit a 3 and the Cougars made 7 of 8 free throws for a 12-4 run to lead 66-54 with 7:22 left. Haws made a jumper and two free throws put BYU up by 22 with 2:25 remaining.