The Warriors (4-2, 2-0 WAC) took the lead for good with a last-minute touchdown drive just before halftime, then padded it with a 35-point second half.
Moniz, the nation's leader in passing and total offense, threw for 376 yards as Hawaii racked up 472 yards of offense.
Fresno State (3-2, 1-1) got 211 yards and two touchdowns passing from Ryan Colburn, who was intercepted three times and sacked three times.
Salas finished with nine catches for 148 yards and two touchdowns. He also scored on a fumble recovery in the end zone on Hawaii's opening drive of the third quarter.
Green rushed for 96 yards on 13 carries.
After scoring on its final possession of the first half, Hawaii opened the third quarter with an eight-play, 73-yard touchdown drive.
When Royce Pollard fumbled into the end zone after making a reception for 21 yards, Salas fell on the loose ball for a 21-10 Warriors lead.
A 38-yard touchdown run by Green made it 28-10 after Colburn threw his second interception.
Following a Bulldogs field goal, Green's 14-yard touchdown run padded Hawaii's lead to 35-13 with 2:38 left in the third quarter.
Hawaii scored touchdowns on its first and final possessions in a first half that featured nine punts and fewer points than expected.
Moniz gave the Warriors a 14-10 halftime lead by directing a five-play, 71-yard drive in the final 1:19 of the second quarter. Following two timeouts and an incompletion, Moniz, a former walk-on, found Salas in between two defenders in the end zone from 8 yards out.
Hawaii's go-ahead drive came in response to a four-play, 65-yard drive by Fresno State, highlighted by Colburn's 50-yard touchdown pass to Jalen Saunders.
Moniz's first touchdown pass to Salas, from 30 yards, put the Warriors ahead 7-0 with 9:57 remaining in the first quarter.