Ikaika Woolsey threw for a touchdown and ran for two more for the Rainbow Warriors (3-10), who led 28-10 early in the third quarter and weathered the Warhawks' rally.
Defensive lineman Lorenzo Jackson fell on Hawaii's errant snap in the end zone late in the fourth quarter to put Louisiana-Monroe (1-11) in a position to tie with a 2-point attempt. The conversion failed as Earnest Carrington's pass attempt was incomplete to Harley Scioneaux.
Hawaii converted three first downs to run out the final 3:03 and end its season with a victory after going winless in the Mountain West Conference.
Carrington finished 27 of 44 for 234 yards and two touchdowns. The Warhawks finish their season next Saturday, hosting New Mexico State.