Marshall's second scoring run gave Auburn a 27-9 lead in the third quarter. 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 Bo 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.
Auburn (4-1, 2-1 Southeastern Conference) already has topped its win total from last season, when it finished 3-9 overall and 0-8 in the SEC.
Ole Miss (3-2, 1-2), coming off a 25-0 loss at No. 1 Alabama, has lost two straight.
First-year coach Gus Malzahn has led a quick turnaround as the Tigers earned their first win over a Top 25 team since beating No. 10 South Carolina in 2011.
Marshall, a transfer from Garden City Community College, had 5-yard scoring runs in the second and third quarters. He completed 11 of 17 passes for 93 yards.
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.
Marshall's role has evolved during his first season. He was given an increased number of carries for the third straight week. He displayed his ability to create big plays on the ground, faking handoffs to Tre Mason, who ran for 77 yards and a touchdown.
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 Laquon 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.
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.
Marshall's big game gave Auburn its school-record fourth 100-yard rusher of the season, following Corey Grant, Artis-Payne and Mason.
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.
McKinzy and other Auburn players were chasing Wallace, who escaped the rush and completed a pass.
Players from both teams stood and watched as medical personnel immobilized McKinzy on a flat board before he was placed on a stretcher. He was still wearing his helmet as he was carted off the field and taken to East Alabama Medical Center in Opelika, Ala.
Freshman defensive tackle Montaviuis Adams hurt his knee on the same play and did not return.