James Farris and Mathew Troupe combined to limit the Gamecocks to three hits as the Wildcats won their fourth title overall. The others came in 1976 and 1980.
Dixon, who entered the game in the sixth inning, sent a grounder down the third-base line past LB Dantzler for his first hit of the CWS.
Tyler Webb relieved Matt Price (5-5), and Trent Gilbert drove in his second and third runs of the game with a two-out single that broke open the game.
South Carolina was trying to become the first team in 40 years to win three consecutive national titles.
The Gamecocks loaded the bases against Troupe (6-1) in the ninth but couldn't score.