Morgan scored five of Cal Poly's final seven points in regulation, but missed an open 3-pointer at the buzzer. His teammate Brian Bennett knotted the game at 61-all with 1:16 left to force overtime.
Morgan hit two 3-pointers in overtime.
Bennett led Cal Poly (8-5, 1-0 Big West Conference) with 20 points. Morgan hit all eight of his free throws and finished with 17 points.
Aaron Valdes scored 20 points for Hawaii (12-5, 0-1). The Rainbow Warriors forced Cal Poly into a season-high 18 turnovers.
Cal Poly jumped out to an early 16-6 lead after holding Hawaii to just two field goals in the first eight minutes. Hawaii stayed close despite shooting 24 percent in the half and trailed 30-23.