Texas A&M led by only a point at halftime, but scored on its first three drives of the second half — on drives of 91 and 89 yards before Manziel threw a short pass to Ryan Swope on fourth-and-5 that turned into a 33-yard TD and a 34-13 lead.
Oklahoma (10-3), which like the Aggies entered the game with a five-game winning streak, went three-and-out on its first three drives after halftime in what was quarterback Landry Jones' 50th and final career start.
"Feel just disappointed that he's going out this way, getting beat like that," Sooners center Gabe Ikard said.
Jones completed 35 of 48 passes for 278 yards with a touchdown and an interception. He won 39 games and three bowls for the Sooners, in a career that started on the same field in the 2009 season opener when he replaced injured Heisman winner Sam Bradford in the first college game at Cowboys Stadium.
But Jones missed out becoming only the third NCAA quarterback to go 4-0 as a starter in bowl games.
"It was obvious tonight that we didn't play the way we should have played," said Jones, whose frustration was evident when he yelled at a teammate after a failed fourth-down play. "We couldn't run it. We couldn't throw it. It happens, you know."
SEC teams have won the last five Cotton Bowls, all against Big 12 teams, and nine out of 10. That included Texas A&M's loss to LSU only two years ago.
It had been six weeks since the Aggies played their last game, and four weeks since Manziel became the first freshman to win college football's highest individual award.
Manziel got it started with an electrifying 24-yard run on third down on the opening drive. Then on a third-and-10, Manziel rolled to his left and took off, juked around a defender and got near the sideline. He tiptoed to stay in bounds and punctuated his 23-yard score with a high-step over the pylon for a quick lead.