Cox hit Aron White on touchdown passes of 24 and 2 yards in the second half as the Bulldogs (8-5) pulled away for their fourth straight bowl victory. It was the fourth straight postseason loss for the Aggies (6-7), who have not won a bowl since 2001.
Georgia blocked two kicks, Brandon Boykin tied the Southeastern Conference record with his third kickoff return of the season and Cox threw his first touchdown pass after the snap sailed over the Texas A&M punter's head in the third quarter.
The Bulldogs sealed the win by intercepting Jerrod Johnson twice in the third quarter.
White tied the Independence Bowl record for touchdown receptions, sharing it with four others.
Special teams led directly to 24 points for the Bulldogs, who also blocked an early field goal attempt and got a 49-yard field goal from Blair Walsh.
The game was billed as an offensive showdown, but a shootout never developed. The teams had more punts than first downs in the first 25 minutes of the game.
Texas A&M finally got moving in the waning moments of the second quarter behind Johnson. He led a nine-play, 75-yard drive that included passes of 14 and 41 yards before the quarterback was flushed from the pocket, rolled left and fired a 15-yard touchdown pass to Jamie McCoy with 2:33 left in the half.
Georgia answered immediately, however, when Boykin returned the kickoff 81 yards up the middle of the field to tie the score. It was his third kickoff return of the season for a touchdown, setting a school record and tying the Southeastern Conference mark held by Tennessee's Willie Gault.
Bulldogs defensive end Demarcus Dobbs sacked Johnson on the next drive, forcing the Aggies to punt. Bacarri Rambo blocked the kick and Vance Cuff recovered it at the 2.
King scored on a dive to make it 14-7 for Georgia despite just 99 first-half yards.
Christine Michael appeared to get the Aggies rolling on Texas A&M's first drive of the second half with a 14-yard touchdown that was set up by Johnson's 19-yard pass on third down.
Their next three drives were disastrous, however.
The first ended on the botched snap, which gave Georgia the ball at the Texas A&M 24. Three plays later Cox hit White with a touch pass down the middle of the field with a rusher in his face to make it 24-14. Johnson threw interceptions on consecutive drives after that.
Georgia was unable to score the first time, but Reshad Jones' 59-yard interception return on the second gave the Bulldogs the ball at the Aggies 28.
Five plays later Cox faked the handoff from the 2, rolled right on a naked bootleg and found the wide-open White in the right corner of the end zone.
King and Shaun Chapas tacked on rushing scores in the fourth quarter to pad Georgia's lead and gave Georgia a share of the bowl record with six touchdowns scored. The Bulldogs also set a record with 30 second-half points.
Johnson, who had a breakout game with four touchdown passes against Texas in the team's regular-season finale, completed 29 of 58 passes for 362 yards and one score. Cox was 15 of 28 for 158 yards. Georgia defensive tackle Geno Atkins was named defensive MVP and White was the offensive pick.
The Bulldogs are 7-2 in the postseason under coach Mark Richt.