Ole Miss (3-2, 1-2 Southeastern Conference), coming off a 25-0 loss at No. 1 Alabama, has lost two straight.
"We have lost the momentum from our start, but that's the game of football," Ole Miss coach Hugh Freeze said.
Auburn had six sacks against Wallace, its high total since 11 sacks against Alabama in 2005.
"We got beat quite a few times," Freeze said. "The thing that's disappointing is not just that you got beat but you got beat quick, right off the ball."
Freeze said maintaining momentum isn't easy when "you play in this conference in the situation we're in, trying to build a program."
Auburn (4-1, 2-1) already has topped its win total from last season, when it finished 3-9 overall and 0-8 in the SEC.
Wallace completed 25 of 48 passes for 336 yards with two touchdowns and two interceptions. Jeff Scott had six carries for 66 yards and Moncrief caught six passes for 122 yards and two touchdowns.
Much of the pressure came as Wallace struggled to find an open receiver.
"I know they weren't blitzing a lot or anything like that," Wallace said. "We will have to go back and look at the film and see what happened."
The Rebels have played four of their first five games on the road, including wins at Vanderbilt and Texas. But two straight losses in night games in the state of Alabama have left the Rebels road-weary.
"I'll tell you this, these road games in a row, these night games and getting back late in the morning, that takes a toll on you," Freeze said.
Freeze was aggressive. Ole Miss was successful on three fourth-down conversions on five tries. Wallace completed a 29-yard pass to Laquon Treadwell on a fourth-and-2 play that set up a field goal late in the first half.
Jeff Scott had a 52-yard gain on another fourth-and-2 play to set up another field goal in the third quarter.
Robenson Therezie scored on a 78-yard interception return to give Auburn a 13-3 lead late in the first quarter.
"It was just a bad throw," Freeze said.
Marshall had 14 carries, including eight that produced first downs.
Tre Mason was the complement to Marshall in Auburn's running attack. Mason ran for 77 yards and a touchdown. Marshall scored on 5-yard runs in the second and third quarters.
Marshall's second scoring run gave Auburn a 27-9 lead, but the game wasn't over. The Tigers lost two turnovers in the fourth quarter to help the Ole Miss comeback attempt.
Ole Miss was held to only three field goals before Wallace threw a 49-yard touchdown pass to Donte Moncrief in the third quarter and added a 12-yard scoring pass to Moncrief midway through the fourth quarter.
Malzahn has led a quick turnaround in his first season as the Tigers earned their first win over a Top 25 team since beating No. 10 South Carolina in 2011.
Marshall, from Garden City Community College, completed 11 of 17 passes for 93 yards.
Defensive ends Carl Lawson and Dee Ford each had two sacks. Defensive tackle Gabe Wright also had two sacks.
Auburn moved 80 yards on its first possession. Marshall completed a 29-yard screen pass to Mason and had a 28-yard run before Mason scored from the 1.
Therezie picked off a pass intended for Treadwell late in the first quarter for his third interception of the season. Therezie's 78-yard return was the eighth-longest in Auburn history.
"I thought he was coming in," said Wallace of Therezie. "He sat. It was a screen, and that is just how it went."
Andrew Ritter kicked field goals of 42, 44 and 22 yards for the Rebels.
Trailing 27-22, Ole Miss had an opportunity to take the lead when Issac Gross recovered a fumble by Auburn's Cameron Artis-Payne at the Ole Miss 40 midway through the fourth quarter.
Auburn's defense quickly responded with an interception by Ryan Smith.
Auburn's Cody Parkey kicked a 23-yard field goal with about 3 minutes remaining.
Auburn linebacker Cassanova McKinzy hurt his neck on the final play of the first quarter and was taken to an area hospital. He was back on the sideline, wearing a neck brace and street clothes, in the third quarter.