Manziel was sitting out because of what the school said was an "inadvertent" violation of NCAA rules involving signing autographs.
His first touchdown came on a 23-yard pass to Mike Evans on A&M's second drive of the half.
Shortly before that, he got into it with a Rice defender, appearing to mimic signing an autograph while getting up from a tackle. He ended his day by getting yanked following an unsportsmanlike conduct penalty for pointing at the scoreboard after a TD pass in the fourth quarter.
He was replaced by Matt Joeckel on A&M's last drive.
Joeckel started at quarterback for A&M and threw for 190 yards and a touchdown to help the Aggies to a 28-21 lead at halftime.
Manziel came in on Texas A&M's first offensive play of the second half and the Aggies capped his first drive with a 44-yard field goal.
He had been investigated for allegedly accepting money for autographs from memorabilia brokers, a violation of NCAA rules that could have led to a much longer suspension.
Instead, the first freshman to win the Heisman only had to sit out the first two quarters to start a season that followed a special one: Not only did he win the Heisman, but he set numerous school and Southeastern Conference records while leading the Aggies to an 11-2 mark and a victory over No. 1 Alabama.
Manziel's first play of the season was a 12 yard run and he also scrambled on the second one, going seven yards. He was sacked on third down and the Aggies settled for the field goal.
Manziel extended A&M's lead to 38-21 with the touchdown pass to Evans.
Ben Malena grabbed an 18-yard pass from Manziel early in the fourth quarter to extend the lead to 45-28.
Rice failed to convert on fourth down on its next drive and Manziel took advantage of the short field two players later when he hit a wide-open Evans in the end zone for a 9-yard touchdown. Then he got a flag.
Asked afterward if he was ready to pull Manziel at that point, before the penalty, Texas A&M coach Kevin Sumlin said: "Nope."
For Rice, Taylor McHargue threw for 180 yards with two touchdowns and two interceptions and Charles Ross had 107 yards rushing with two scores for the Owls.
Ross got Rice within 10 points with a 1-yard run seconds into the fourth quarter.
The Aggies struggled early in the first half, possibly due to the suspensions of five defensive starters: Cornerbacks Deshazor Everett and De'Vante Harris, tackle Kirby Ennis, end Gavin Stansbury and linebacker Steven Jenkins. Backup safety Floyd Raven also was suspended.
The two-game penalties for Harris, Stansbury, Jenkins and receiver Edward Pope were announced just minutes before kickoff, meaning their first game action will be against top-ranked Alabama on Sept. 14.
Everett's suspension was for a half. He started on defense after the break but was ejected in the fourth quarter for targeting.
The Aggies wore special helmet stickers to remember defensive lineman Polo Manukainiu, who was killed in a New Mexico car crash along with two others late last month. The sticker is black and white and features his No. 90 with designs in the number that were inspired by his Tongan heritage.
The Aggies relied on the running game in the second quarter to complete a touchdown drive with a 1-yard run by Carson to even the score. Malena had 82 yards rushing with a touchdown and a touchdown catch. Tra Carson added 76 yards rushing and two touchdowns for the Aggies.
A&M's first lead came on a 71-yard catch and run by freshman Ricky Seals-Jones that made it 21-14. Carson pushed the lead to 28-14 with his second score on a two-yard run.
Rice jumped out to a 7-0 lead after a 1-yard run by Ross. That drive was helped by a career-long 57-yard run by McHargue. With Manziel watching from the sidelines sporting a visor, A&M evened it up when Ben Malena scored on a 4-yard run later in the first quarter.
The Owls took a 14-7 lead when McHargue found Charles Ross on a 19-yard touchdown pass with seven minutes left in the first quarter.