Shaw went 14-of-22 for 272 yards and ran in a 10-yard touchdown in the second quarter that gave the Gamecocks (8-2, 6-2 SEC) a lead they never lost.
Bruce Ellington caught five passes for 104 yards and a TD for South Carolina and D.J. Swearinger returned an interception 69 yards in the third quarter to extend the lead to 31-10.
Arkansas (4-6, 2-4) needs to beat both Mississippi State and LSU in its final two games to become bowl eligible.
Tyler Wilson was 26-of-41 passing for 277 yards and two touchdowns but was intercepted twice in the second half.