The Heisman Trophy candidate eclipsed the SEC mark for total career offense, completing 32-of-44 passes for 372 yards and an interception, while running the ball 12 times for 67 yards.
Manziel broke Cam Newton's conference record of 4,161 total yards in a single season.
The performance came after the signal-caller injured his left knee in the second quarter. He returned to the game wearing a brace.
The victory was the fifth straight for Texas A&M (10-2, 6-2 SEC).
Missouri (5-7, 2-6) was led by Corbin Berkstresser, who finished 20-of-38 for 276 yards with a pair of touchdowns and an interception.