Tyler Lamb added 18 points for LBSU (13-14, 9-4 Big West).
Davis Rozitis hit a jumper with 3:32 remaining to give Hawaii a five point lead before Lamb hit a 3 just 25 seconds later to make it 60-58.
Christian Standhardinger made 1 of 2 free throws to push the Hawaii (19-9, 8-6) to three with 1:48 left.
On the next 49ers possession, LBSU missed a pair of jumpers but pulled down a couple offensive rebounds before a jumpshot by Jennings made it a one-point game with 1:08 remaining.
Long Beach State got another stop and Hammonds corralled his own miss before knocking down the game winner.
Standhardinger scored 17 points and now has 1,001 points in his career at Hawaii.