Shaw completed 19-of-28 passes for 219 yards and the South Carolina (5-1, 3-1 SEC) defense limited Arkansas (3-4, 0-3) to a first-quarter touchdown and 30 passing yards.
Mike Davis carried 19 times for 128 yards and a TD for the Gamecocks, who racked up 537 yards of total offense to 248 for the Razorbacks, who lost their fourth consecutive game.
South Carolina's star defensive end Jadeveon Clowney was back on the field after missing last week's game with an injury, but he didn't have much opportunity to show his stuff since the offense held the ball 43 minutes, 25 seconds compared to 16:35 for Arkansas.
Alex Collins ran for a 6-yard touchdown that gave Arkansas a 6-0 lead early in the first quarter, but it was the last time the Razorbacks would score. Brandon Allen completed 4-of-12 passes for 30 yards and was intercepted once.