The Rebels pulled the redshirt off Patterson, the highly regarded recruit, to start in place of Chad Kelly, who suffered a season-ending knee injury last week.
Mississippi (5-5, 2-4 Southeastern Conference) trailed by 15 entering the fourth quarter before Patterson got going.
A 13-yard touchdown reception by Josh Reynolds put A&M up 28-19. Patterson then connected with Van Jefferson on a 32-yard reception for his second TD pass of the quarter to cut the lead to 28-26 with 5:17 remaining.
A&M (7-3, 4-3) had to punt and Patterson moved the offense into position for Wunderlich's game-winning field goal.
The Aggies had a chance to win it late, but Jake Hubenak was intercepted by Deontay Anderson to secure the victory. Hubenak was making his first start this season in place of Trevor Knight, who injured his shoulder last week.
Early in the fourth quarter Patterson looked like he was channeling A&M Heisman Trophy winner Johnny Manziel when he scrambled to one side, avoided the rush and ran the other way before launching a 6-yard touchdown pass to Damore'ea Stringfellow to get Ole Miss within 21-13.
On their next drive Stringfellow reached out with his right hand and tipped the ball with his fingertips before reeling it in with one hand for an eye-popping 40-yard reception. Akeem Judd's 21-yard run made it 21-19, but the two-point conversion failed.
The Aggies led 21-6 at halftime thanks to two touchdown runs by Keith Ford.
The Rebels had turnovers on their first two possessions of the second half, but Texas A&M couldn't convert either of them into points. Patterson threw an interception on the first one and Jason Pellerin was sacked and fumbled after that.
MISSISSIPPI: Patterson showed why he was the No. 1 rated dual-threat quarterback recruit by Rivals last year, and should make Ole Miss fans excited about his potential for next season. But first he'll look to get the Rebels a win over Vanderbilt next week to make them bowl eligible for the fifth straight season.
TEXAS A&M: Hubenak couldn't make plays in the second half and the Aggie struggled with tackling yet again. He'll have to improve if Texas A&M hopes to beat LSU in two weeks and salvage this season that started out with six straight wins before the Aggies dropped three of their last four games.
MISSISSIPPI: The Rebels visit Vanderbilt next Saturday.
TEXAS A&M: The Aggies take a break from SEC play by hosting Texas-San Antonio next Saturday before wrapping up the regular season against LSU on Thanksgiving night.