Sheriff Drammeh added 11 points and six rebounds for the Rainbow Warriors (12-5, 3-1 Big West Conference), while Michael Thomas scored 11.
Max Heidegger topped the Gauchos (12-5, 1-2) with 22 points. Heidegger, who leads the conference with a 21.6 scoring average, had just three points at halftime. Jalen Canty chipped in with 16 points and eight rebounds, Leland King II and Gabe Vincent added 11 points apiece and Marcus Jackson scored 10 as all five UCSB starters scored in double figures.
Stepteau and Drammeh combined to score 19 in the first half as Hawaii shot 58 percent from the floor and took a 42-33 lead into intermission.
Gibson scored seven in a 13-6 run to open the second half to give the Rainbow Warriors a 55-39 lead. But Heidegger found his shooting touch and scored 11 in a 13-0 run to pull the Gauchos within 55-52 with 12:21 left to play. The Gauchos hung tough and trailed 64-63 with 4:10 left on a Vincent layup, but Jack Purchase knocked down a 3-pointer and Drew Buggs hit from long range to give Hawaii a 72-65 lead with 51 seconds left. Heidegger hit three free throws and a 3-pointer to cut the deficit to three with 10 seconds left, but Johnson made 1 of 2 free throws to offset Jackson's 3-pointer at the buzzer for UCSB.