The 1963 edition to the Sugar Bowl featured the 3rd ranked Ole Miss Rebels, and the 6th ranked Arkansas Razorbacks. Behind a solid win, Ole Miss locked up its second national championship in three years.
Ole Miss took the early 3-0 lead in the second quarter, after a 30 yard Irwin field goal. Arkansas answered with a 30-yard field goal from Tom McKnelly, tying the game at 3-3. Quarterback Glynn Griffing threw a 33-yard touchdown pass to Louis Guy, giving Ole Miss a 10-3 lead at halftime.
In the third quarter, Razorback quarterback Billy Moore, who was eventually knocked out of the game by Ole Miss' Buck Randall, found Jesse Branch for a 5-yard touchdown pass that tied the game at 10. Glynn Griffin scored on a 1-yard touchdown run giving Ole Miss a 17-10 lead. A 22 yard Tom McKnelly field goal in the fourth quarter, pulled the Razorbacks to 17-13, but Ole Miss held on for the win. Glynn Griffin was named Sugar Bowl MVP.