Carr had scoring throws of 30 yards and 9 yards to Josh Harper and L.J. Jones returned an interception 56 yards for a score that put the Bulldogs ahead 42-3 midway through the third quarter.
But Hawaii, with three touchdown passes from Sean Schroeder and two scoring runs by Steven Lakalaka, ran off 34 consecutive points to make the final score close.
Carr completed 33-of-47 passes for 324 yards while Harper caught nine passes for 123 yards. Marteze Waller rushed for 95 yards and two more scores as Fresno State (4-0 overall, 2-0 Mountain West Conference) had just enough points to keep Hawaii (0-4, 0-2) winless.
Harper and Waller each scored in the first quarter and Carr had a 1-yard run for another touchdown before Hawaii got on the board with a 48-yard Tyler Hadden field goal late in the first half.
Harper and Waller scored in the third period and Jones took the interception back for the 39-point lead with 6:15 left in the third period.
Schroeder replaced Ikaika Woolsey at quarterback and led the charge back, hitting 17-of-27 passes for 321 yards and three touchdowns. Lakalaka's second touchdown came with 7:51 left.
Hawaii had two more chances after that but Fresno State forced a three-and-out and intercepted Schroeder to end the upset threat,