Manziel suffered through a tough night until late in the fourth quarter, when he led two touchdown drives. He rushed for a 29-yard touchdown on the first and then found Ryan Swope for a 20-yard TD pass with 1:46 remaining for the go-ahead score.
Texas A&M (4-1, 2-1 Southeastern Conference) won despite a season-high six turnovers, including four fumbles and two interceptions.
Ole Miss (3-3, 0-2) made a final drive but Texas A&M's Toney Hurd, Jr., intercepted a Bo Wallace pass and the Aggies were able to run out the clock.
The Rebels lost their 16th straight conference game dating back to 2010. Jeff Scott rushed for 108 yards and a touchdown. Wallace completed 20 of 34 passes for 305 yards, one touchdown and two interceptions. He also rushed for a touchdown.
Ole Miss had a 27-17 lead midway through the fourth quarter and Texas A&M pinned on its own 1-yard line with less than eight minutes remaining.
But Manziel connected on a 32-yard, third-down pass to Mike Evans to give the Aggies some breathing room. Then in just two plays, Texas A&M drove the rest of the field for a stunning touchdown. Ben Malena gashed the Rebels' defense for 36 yards before Manziel rushed for a 29-yard score -- dancing past several Ole Miss would-be tacklers -- to make it 27-23.
On the ensuing drive, first-year Ole Miss coach Hugh Freeze made a questionable decision to go for it on fourth-and-1 in his own territory.
It turned out to be a disastrous call.
Scott was stuffed at the Ole Miss 39 and Texas A&M needed just four plays for Manziel to find Swope for the game-winning score.
Manziel completed 17 of 26 passes. Mike Evans caught eight passes for 105 yards.
Manziel -- the 6-foot-1, 200-pound freshman with a penchant for highlight-reel plays -- was coming off a breakout game against Arkansas that included 557 total yards and four touchdowns.
He looked much more mortal against the Rebels -- at least for a while. There were a couple of huge plays, like his 38-yard scramble in the third quarter to push the Aggies deep into Ole Miss territory. But his risk-taking had a downside, too, like four plays later when he lost a fumble on the Ole Miss 21 to stop an almost certain scoring drive.
Manziel made another crucial mistake early in the fourth quarter, deftly avoiding the Ole Miss rush before making a bad pass over the middle that was intercepted by Cody Prewitt.
But the precocious quarterback wasn't fazed, and engineered the stunning comeback.
Texas A&M struck first on the opening drive after Malena burst through a huge hole and ran untouched 59 yards for a touchdown and 7-0 lead.
But the Ole Miss defense tightened considerably after that hiccup, while the offense improved as the first half progressed.
The Rebels took a 17-10 lead on a 14-yard run by Wallace -- one play after he hit Randall Mackey on a 68-yard pass.
Then the Aggies fumbled on their own 35 -- their third turnover of the half -- and the Rebels had a chance to create some separation on the scoreboard.
But Ole Miss couldn't take advantage. Wallace was hit as he threw and the ball fell right to Texas A&M linebacker Steven Jenkins, who ran for the easy 37-yard touchdown that tied the game at 17 going into halftime.