Bryce Massanari and Colby May hit home runs and finished with two hits apiece. Rich Poythress, the reigning National Hitter of the Week, went 2-for-4 with his league-leading 48th RBI.
Jason Leaver (3-0) pitched 3.0 innings and allowed one run on four hits to earn the win. Justin Earls and Michael Palazzone combined to throw 3.0 shutout innings, and Dean Weaver worked the ninth to earn his third save in as many games and fifth overall.
Clemson trailed 6-4 entering the ninth, and scored to get within a run and had the tying run on first but Weaver struck out Brad Miller to end the game.
"We were good enough to win tonight," Georgia coach David Perno said. "They had better pitching; he was a weekend starter for them, but I was proud of our guys. We need more out of the offense in the future. I didn't see the fire.
Jeff Schaus put Clemson ahead 1-0 with a two-out home run in the top of the first before Massanari homered for the sixth time this year and the fourth time in six games in the second inning to knot the score at 1-1.
Clemson's first two batters reached to start the third and with two outs, Zach Cone made a leaping catch over the wall in right center to rob Brad Miller of a three-run homer.
Georgia sent 10 players to bat and scored four runs in the third. After a one-out walk to Michael Demperio, the Dogs reeled off five straight singles by Johnathan Taylor, Peter Verdin, Poythress, Massanari and Joey Lewis to take a 5-1 lead.
Colby May blasted a solo home run in the sixth, his eighth of the season, to give Georgia a two-run lead again. Clemson cut the deficit to 6-5 with a two-out RBI single by Kyle Parker, but Miller struck out for the final out.
Chris Dwyer (2-2) allowed five runs on eight hits in 3.0 innings to take the loss.
The Bulldogs and Tigers will play again tomorrow at Clemson at 7 p.m. on CSS.