Oregon State took the lead for good, 40-38, on Cunningham's two free throws 11 seconds after halftime.
A Starks 3-pointer later put the Beavers ahead seven, and Oregon State got the lead to 10 for the first time, 60-50, on two more Cunningham foul shots with 12:23 remaining.
The Beavers went ahead by as many as 16 before Cal scored 12 straight, including two 3-pointers by Allen Crabbe and a four-point play by Gutierrez, to close within 77-73 with five minutes left.
But the Beavers scored the next four and the Golden Bears got no closer than six the rest of the way.
Hawaii will play in the Fox Sports Pearl Harbor Invitational in December, part of the 75th anniversary of the attack on Pearl Harbor.
An attorney representing ex-Michigan State basketball star Mateen Cleaves wants a judge to disqualify the Wayne County prosecutor's office from Cleaves' sexual assault case.
The Big East has joined the ACC, Atlantic 10 and Colonial Athletic Association in forming a men's basketball officiating alliance.