Mississippi State (10-21) advanced to a second-round game Thursday against No. 5 seed Tennessee (19-11), which has won eight of its last nine games.
The Bulldogs have won three of their last four games, though they had dropped 13 straight before that. South Carolina (14-18) has lost five of its last six.
Thomas scored eight points during a 13-0 run midway through the first half that broke a 13-13 tie and put Mississippi State ahead for good.
Colin Borchert and Roquez Johnson scored 11 points apiece and Gavin Ware added 10 for Mississippi State.
Bruce Ellington scored 13 points and Laimonas Chatkevicius matched a career high with 11 points for South Carolina.