Greenlee, who came into the game with eight career scoring passes, completed 20 of 35 for 285 yards - all career highs.
Hawaii (2-9, 0-7 Mountain West) finished with 437 total yards, but committed four turnovers and 11 penalties - for 132 yards - on its way to its eighth loss in a row.
Ikaika Woolsley's 14-yard touchdown pass to Makoa Camanse-Stevens early in the second quarter capped a seven-play, 75-yard drive by Hawaii and tied the game at 7.
Fresno State scored touchdowns on three of its next four drives, including touchdown passes of 28 and 25 yards from Greenlee to Da'Mari Scott, to take a 28-7 lead into halftime.
Six Bulldogs combined for 170 yards rushing on 51 carries as Fresno State held the ball for 37 minutes, 13 seconds.