AJ McCarron completed 25 of 32 passes for 180 yards with an interception for Alabama, which came in ranked last in the league in rushing. Alabama was held to 36 rushing yards in building a 9-0 halftime lead but gained another 218 on the ground in the second half.
Bo Wallace was 17-of-30 passing for 159 yards for the Rebels.
The Rebels' fast-paced offense came in averaging 38 points and 490 yards, but never got going and managed just 46 yards on 25 rushes. Alabama's C.J. Mosley made a tackle in the end zone in the fourth quarter for a safety, and Drake's 50-yarder came on the next play.
Jeff Scott, who was averaging 110 yards a game and 9.4 per carry, was held to 28 yards on eight attempts.
Alabama's more plodding style helped the Tide monopolize the ball for 38 minutes, 29 seconds.
Yeldon, who had 17 carries, breathed life into the running game on the second play after halftime.
He burst through the line and spun away from a defender before winning a footrace to the end zone for a career-long 68-yard TD.
The performance came a week after team leaders McCarron, Mosley and Vinnie Sunseri addressed the team following an unimpressive showing against Colorado State. Then Saban, held individual meetings with players during the week.
None of the talking paid immediate dividends on the scoreboard. Seeking more respect nationally, Ole Miss trailed just 9-0 at halftime. Alabama's offense repeatedly stalled but Cade Foster hit field goals of 28, 42 and a career-long 53 yards.
His 42-yarder came on the final play of the half after Ole Miss helped Alabama move downfield over the last 3:09 with a pass interference penalty and two timeouts, hoping to get the ball back.
The Rebels had several gambles fail, converting just 1 of 4 fourth-down tries.
They had a chance to close the gap early in the fourth quarter when Cody Prewitt intercepted McCarron's pass at the Alabama 31. It was McCarron's third interception of the season, matching last year's total.
The Rebels made it to the 13 and got another shot thanks to a false start before Wallace's fourth-and-5 pass fell incomplete. Coach Hugh Freeze went for it again, but Deion Belue broke up the throw headed toward the goal line.