Wallace threw both of his touchdown passes on long completions to Ja-Mes Logan, who finished with six receptions for 122 yards. Ole Miss (5-3) won its second straight game, finishing with 569 total yards.
Ole Miss led 17-0 after one quarter, 24-7 at halftime and erased any remaining doubt with 21 points in the third quarter.
It was an easy victory for the Rebels, who needed one after a brutal month of games that included losses to Alabama, Auburn and Texas A&M, as well as last week's upset victory over LSU.
The Rebels took a 14-0 lead in less than seven minutes. The first touchdown was a perfectly placed 37-yard throw from Wallace to Logan while the second was a 40-yard run by Walton.
Idaho came into the game as a 41-point underdog and had already been blown out by programs like North Texas and Wyoming. Even worse, the Vandals started Davis, their third string quarterback, on Saturday because of injuries to Chad Chalich and Joshua McCain.
But they stayed competitive in the first half and put together a 75-yard drive -- capped by a 2-yard TD run by Davis -- to pull within 17-7 early in the second quarter.
Ole Miss led 24-7 at halftime and quickly added to the advantage with a 65-yard heave from Wallace to Logan to make it 31-7 with 9:26 left in the third quarter.
The Rebels now have a week to rest before a Nov. 9 game against Arkansas in Oxford. A win would give Ole Miss bowl eligibility for the second straight season.
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Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.
Mike Bercovici passed for 273 yards and two touchdowns and ran for another score, and Arizona State got its season back on track with a 38-23 victory over No. 7 UCLA on Saturday night.
Florida State running back Dalvin Cook exited in the first quarter of the Seminoles' 24-16 win over Wake Forest with a left hamstring injury. He is day-to-day.
As if things weren't going bad enough at Texas, the Longhorns appear to have players on Twitter during lopsided losses and jabs at their coach accidentally being sent from other nearby teams.
Tulane long-snapper Aaron Golub became the first legally blind person to play in a Division I football game Saturday, according to the school.