He was sharp from the outset, leading the Rebels to a 28-0 lead after one quarter. He completed 20 of 25 passes during the game.
Ole Miss had two interceptions in the third quarter that ended any hope of a Fresno State comeback. Trae Elston's was returned for a 38-yard touchdown, which was his second straight game with an interception return for a score.
Ole Miss finished with 607 total yards.
It was another brilliant offensive display by the Rebels, who scored 76 points in their opener against UT Martin last week. The 149 points over a two-game stretch are the most in school history.
Adeboyejo caught five passes for 120 yards and his three touchdowns.
Robert Nkemdiche, who usually plays on the defensive line, scored a touchdown for the second straight game. This one was a 1-yard run in the third quarter.
Kelly left little doubt about the quarterback race with a productive first half that included 305 yards passing and four touchdowns. He also ran for a 4-yard touchdown.
The 6-foot-2, 215-pound junior showed his touch on a 14-yard touchdown pass to Cody Core in the corner of the end zone and then flashed good arm strength on three straight touchdown throws to Adeboyejo, who scored from 16, 50 and 44 yards out.
While Kelly was nearly perfect, his backups were not. Kincade had some decent moments but looked uncomfortable in the passing game. Fresno State's Shannon Edwards picked off a Buchanan pass and ran 56 yards for the touchdown.
That was the first of a few gaffes that allowed Fresno State a brief chance to get back into the game. The Bulldogs pulled within 35-14 by halftime.
After Ole Miss' Carlos Davis fumbled a punt deep in Rebels territory, Fresno State looked like it might pull within two scores. But C.J. Johnson, an Ole Miss linebacker, intercepted a Virgil pass and ran it back 70 yards to set up another Rebels touchdown and the rout was just getting started.