Arkansas (1-4, 0-2) led 10-7 after one quarter before the Aggies (3-1, 1-1) scored 51 straight points to take the lead and cruise to the win. It broke a three-game losing streak to the Razorbacks, who beat A&M 42-38 last season after trailing 35-17 at halftime.
Manziel added 104 yards rushing to also break the school and SEC records for yards of total offense with 557.
Tyler Wilson threw for 373 yards and a touchdown, but he threw two interceptions as Arkansas was shut out after the first quarter.
Steven Terrell had two interceptions and Tramain Jacobs returned a fumble for a touchdown for Texas A&M.
Ryan Swope had five receptions for 141 yards and a touchdown, recording his school-record 10th career 100-yard game. Thomas Johnson added 108 yards receiving and Mike Evans had 83 yards and a score as A&M piled up 716 yards of total offense.
Manziel, a freshman, has accounted for 15 touchdowns in the Aggies' last three games.
Texas A&M's 58 points are the most it has scored against the Razorbacks in the 69-game history of the series.
Manziel, who finished 29 of 38, went 5 of 5 on the first drive, capped by a 4-yard touchdown pass to Mike Evans to make it 7-0. Evans bent down to scoop the pass before it hit the ground for his first career touchdown.
The Aggie defense forced a punt, but Taylor Bertolet's 39-yard field goal attempt on the next possession was wide right.
Wilson found Knile Davis on a short pass that he took 64 yards for a touchdown to tie the game about 7 minutes before halftime.
A 26-yard field goal by Zach Hocker gave Arkansas a 10-7 lead near the end of the first quarter.
The second quarter was all A&M, with Bertolet redeeming himself after his early miss with a 46-yard field goal to tie it early in the quarter. His 26-yard field goal about 4 minutes later gave A&M a 13-10 lead.
Terrell's first interception came on the next drive by Arkansas. He fumbled at the end of the return, but it bounced back into his hands to give A&M the ball at midfield. A 29-yard run by Ben Malena got the drive going, and he finished it off with an 11-yard touchdown reception to push the lead to 20-10.
A tough drive by Arkansas where the team fumbled twice, but recovered both times, followed to force the Razorbacks to punt.
The Aggies went deep on the next play, with Manziel using a pump fake and Swope a double move to get behind the defense for an 80-yard touchdown reception.
Things weren't any better for the Razorbacks after halftime, and Wilson's first pass of the second half was intercepted by Terrell. He returned it 30 yards and A&M extended the lead to 30-10 with a 21-yard field goal.
Christine Michael bulled into the end zone on a 10-yard run later in the third quarter to leave A&M up 37-10.
Damontre Moore forced a fumble by Davis, which Jacobs scooped up and returned 28 yards for a touchdown on the Razorbacks' first play after Michael's touchdown.
Manziel capped his scoring for the day when he circled around and even went backward before zipping into the end zone on a 6-yard run with about 10 minutes left to make it 51-10. Trey Williams added a 13-yard touchdown run late in the fourth quarter.
Cobi Hamilton finished with 11 receptions for 162 yards for Arkansas, and Davis had 65 yards rushing.