South Carolina (38-15, 15-12 Southeastern Conference) took an early lead in the second inning with five runs on four hits, including a double by Disher that drove in three.
Tennessee (30-22, 11-14) started off strong with three RBI singles in the first inning, but was held to only seven runs on 15 hits.
South Carolina kept Tennessee from shortening the 6-4 lead in the fourth and turned a grounder into a double play that tagged out Yan Gomes and Jeff Lockwood.
Volunteer Shawn Griffin slugged a pinch-hit, two-run homer in the bottom of the fifth that cut South Carolina's lead to a single run at 7-6.
But Steven Reinhold scored on a double in the fifth and Reese Havens followed with double RBIs to secure the win for South Carolina.
Gamecocks catcher Trent Kline scored from second base on an infield error in the eighth and reliever Curtis Johnson got the save in the bottom of the frame.
Disher hit a two-run homer in the top of the ninth that closed out the scoring at 13-7.
South Carolina pitcher Blake Cooper picked up the win to improve 7-1 and Vols pitcher Craig Cobb fell 7-5 with the loss.