Stafford, a sophomore beginning his first full season as the starting quarterback, was 18-of-24 for 234 yards and two touchdowns with no interceptions.
Georgia (1-0) led 21-14 at halftime and Stafford put the game out of reach with touchdown passes to Bruce Figgins, a freshman tight end, and Michael Moore.
Oklahoma State's Bobby Reid was 16-of-30 for 191 yards with one touchdown and one interception. Reid completed a 20-yard scoring pass to Adarius Bowman in the first quarter.
Mikey Henderson's 63-yard punt return set up Stafford's 9-yard touchdown pass to Moore in the fourth quarter.
There were no turnovers for either team until less than 10 minutes left in the game, when Georgia safety Kelin Johnson intercepted a fourth-down pass by Reid.
Dantrell Savage scored on a 5-yard run with 5:43 left in the first half, but that was the last time the Cowboys' high-powered offense could get into the end zone.
Oklahoma State finished its 2006 season with an Independence Bowl victory over Alabama, but it couldn't come close to a second straight win over a Southeastern Conference opponent.
Georgia had five sacks and kept constant pressure on Reid while holding Savage to 55 yards rushing.
Georgia led 7-0 less than a minute into the game, even though Oklahoma State won the opening coin toss. After being stopped on downs, the Cowboys lined up for the punt, but Zach Allen's snap sailed over punter Matt Fodge's head. Fodge recovered the ball and was hit by Georgia's Mohamed Massaquoi at the 14.
On first down from the 14, Brown fought his way straight through the line for a touchdown.
The Cowboys began their third possession at the Georgia 47 and scored on Reid's pass to Bowman from the 20.
Scoring runs by fullback Brannan Southerland from the 2 with 19 seconds left in the first quarter and by Brown from the 3 midway through the second gave Georgia a 21-7 lead.
A big third-and-21 play helped Oklahoma State cut into Georgia's lead. Reid threw a pass over the middle to Bowman for 28 yards for a first down. Savage vaulted over a tackler in front of the goal line.
A 35-yard pass from Stafford to freshman Knowshon Moreno helped Georgia open the second half with a scoring drive, capped by Figgins' 11-yard catch, for a 28-14 lead.
Moreno led Georgia with 70 yards rushing and caught two passes for 51 yards.
Brown rushed for 48 yards.