A few minutes later, Jaylen Walton sliced through the middle of Idaho's defensive line for a 40-yard touchdown.
It was the beginning of a lopsided 59-14 victory for the Rebels, who relished the easy non-conference night after a month of rough games against the top of the Southeastern Conference.
Now the Rebels have two weeks of rest and preparation before playing Arkansas on Nov. 9 in Oxford.
"It was huge to play that stretch of games and then still come out and win tonight," Wallace said. "Fortunately nobody got hurt and now it's a week of treatment and getting ready for Arkansas."
Wallace threw for 186 yards and two touchdowns, I'Tavius Mathers rushed for 138 yards and another touchdown and Mississippi rolled up 572 total yards. The 59 points were the most for the Rebels since 2008.
Wallace threw both of his touchdown passes to Logan, who finished with six receptions for 122 yards. Logan has been one of the Rebels' most productive receivers throughout the year with 24 catches coming into the game but those were the first two that resulted in touchdowns.
Ole Miss (5-3) won its second straight game. It wasn't a perfect night for the Rebels, who had a second-quarter swoon that allowed the Vandals to pull within 17-7, but they recovered to win handily.
"In the first half, for six minutes, it looked like we wanted to be here," Ole Miss coach Hugh Freeze said. "Then we had 15 minutes of ho-hum, going through the motions. In the second half, we played like I expected we would play."
Idaho (1-7) lost its third straight game. Taylor Davis completed 12 of 30 passes for 166 yards and one touchdown. Dezmon Epps caught five passes for 89 yards and a touchdown.
"I thought our guys fought pretty hard for the most part," Idaho first-year coach Paul Petrino said. "But we've still got a long way to go."
Ole Miss led 17-0 after one quarter, 24-7 at halftime and erased any remaining doubt with 21 points in the third quarter.
Walton added 86 yards rushing and two touchdowns. Backup quarterback Barry Brunetti completed 7 of 7 passes for 94 yards and two touchdowns.
Brunetti has thrown five TDs in his past 13 pass attempts.
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.
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.
"I wouldn't say the defense performed great since we gave up 14 points," Ole Miss linebacker Serderius Bryant said. "The goal was to hold them to zero. But in the end we did what we had to do to stop them from scoring anymore."
Ole Miss led 24-7 at halftime and 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 won despite missing several key starters, including running back Jeff Scott (thigh bruise) and defensive end Robert Nkemdiche (hamstring). Freeze said the upcoming bye week comes at a good time.
"We need it desperately," Freeze said. "We still played without seven starters."
The Rebels are now one win away from being bowl eligible for the second straight season.