MSU (8-4) committed five turnovers and lost quarterback Nick Fitzgerald to a bad ankle injury in the first quarter.
Point Man: Brown made six catches for 167 yards and one touchdown.
Fitzgerald was carted off the field in the first quarter after his leg bent awkwardly when he was tackled on a rushing attempt.
Brown became Ole Miss' single-season leader in receiving yards.
Ole Miss had its third game with two scoring passing plays of 60 or more yards.
Mullen - 69-49 in nine seasons, including 8-4 in 2017, in arguably the toughest job in the SEC - now makes $4.5 million annually at Mississippi State, but according to SI.com's report, "word is the school is willing to bump him up to around $6 million and also making an even stronger financial commitment to his staff". That forced true freshman Keytaon Thompson into action. But Ole Miss recovered the ensuing onside kick.
"We just ran out of time there at the end", Mississippi State coach Dan Mullen said. However, the Bulldogs were not ready to give up the fight and scored with just more than nine minutes remaining in the game. "I'm happy with what we've built".
Ta'amu found Starkville-native A.J. Brown for a 58-yard catch-and-run on the very next play.
Fitzgerald completed just 1 of 5 passes for 12 yards and threw an interception in the game against Ole Miss.
Mullen said after the game that Fitzgerald dislocated his ankle, but didn't have any further information.
After the game, players chanted "We want Luke!" in the locker room and Brown said he thought Luke should be the coach going forward. The Rebels will also decide if they'll keep Luke or turn to someone else to lead the program.