"We just never say die," senior right fielder Bobby Felmy said. "We've been saying all year, ‘You never back a dog into a corner.'"
The Bulldogs (47-21) will play second-seeded Rice (55-11) on Saturday at 2 p.m. Eastern. The No. 15 Gamecocks finished the season 41-25.
Georgia's players piled onto each other in the middle of the field after the game.
"These kids are unbelievable," Georgia coach David Perno said. "It's about them. They just willed it."
The Bulldogs won a coin toss after Sunday night's win and could have been the home team Monday but instead chose to be the visitors and stay in their regular dugout. If the strategy had backfired, Perno would have been second-guessed for weeks, but the move didn't seem risky to the Bulldog coach, he said.
"You don't gamble with these guys," he said. "They're the real deal."
The Bulldogs extended what may be the nation's most impressive streak by winning their fifth straight elimination game in this tournament. They are 8-1 in elimination games this year, including the SEC Tournament.
"You have to be good to be able to do that," South Carolina coach Ray Tanner said. "They've got a great makeup right now. They've got the ingredients to be dangerous in Omaha. The best team in this Super Regional definitely won."
Georgia now is 11-0 all-time at Foley Field in NCAA elimination games. It has made its five CWS appearances in just five seven overall NCAA Tournament berths.
Monday's victory followed the pattern Georgia has followed throughout this run. Dawdle early, rally late and hand the game over to a stellar bullpen.
Georgia scored the tying run in the fifth inning and the go-ahead run in the sixth both without the benefit of a hit. South Carolina starter Wynn Pelzer had a 3-2 lead with two outs in the bottom of the fifth inning, but he hit Josh Morris with a pitch, walked Bobby Felmy and Jason Jacobs and then hit designated hitter Matt Olson to drive in Morris and tie the score 3-3.
In the sixth inning, Bulldog second baseman Matthew Dunn walked, moved to second on another walk, advanced to third on a fly ball to the outfield and scored on a wild pitch to put Georgia up for good, 4-3.
Those gifts ignited the Bulldogs, who sent 11 batters to the plate in the next inning and got all seven RBIs from their starting outfield of Felmy (home run and triple, three RBIs), Joey Side (two-run triple) and Jonathan Wyatt (two-run single.) The inning was Georgia's second-most prolific of the season.
Pelzer (5-5) took the loss after giving up seven hits and seven walks in six innings.
"His stuff was outstanding," Tanner said. "He had a little trouble harnessing it at times, but he battled for us."
It was another impressive offensive night for Side, who broke the school record for single-season hits with No. 109 and 110. (Chaz Lytle held the previous record at 108.)
Georgia freshman Trevor Holder (5-3), who relieved starter Jason Leaver, got the victory by pitching a scoreless fourth and fifth inning.
With the win, the Bulldogs tied the 2001 College World Series team for second-place on the school's all-time victories list. The 1990 national championship team holds the record with 52 wins.
Perno was a member of the 1990 team and has a connection to each of the previous four Bulldog teams that made a trip to the College World Series.
"I talked to these guys before the game, and I told them there wasn't a more deserving team to go to Omaha than this one," he said. "They needed to find a way to get it done because they deserved it more than any other team here."