With 99 percent of precincts reporting, MSNBC said Gingrich took 40 percent of the votes in the first-in-the-South primary, with former Massachusetts Gov. Romney a distant second at 28 percent.
CNN exit polling indicated South Carolina voters see Gingrich as more electable than Romney, based on his debate performances.
"People completely misunderstand what's going on. It's not that I'm a good debater. It's that I articulate the deepest-felt values of the American people," Gingrich told supporters during his victory speech.
Gingrich praised Santorum, Paul and even Romney, calling him a "good example of America," touting Romney's success in business and in organizing the 2002 Salt Lake City Winter Olympics. He then turned his sights on President Obama.
"This is the most important election of our lifetime. If Barack Obama can get re-elected after this disaster, just think how radical he would be in a second term. …
"The centerpiece of this campaign, I believe, is American exceptionalism versus the radicalism of Saul Alinsky," the founder of modern community organizing, Gingrich said.
Obama, who touted his work as a community organizer during the 2008 campaign, gets his support from "people who don't like the classical America," Gingrich said, calling Obama the "most effective food-stamp president in history."
"We don't have the kind of money that at least one of the candidates has, but we do have ideas, and we do have people. And we proved here in South Carolina that people power with the right ideas beats big money, and with your help, we're going to prove it again in Florida," Gingrich concluded.
Romney earlier acknowledged Gingrich's victory Saturday but also took aim at the new front-runner, comparing him to President Obama.
"President Obama has no experience running a business and no experience running a state. Our party can't be led to victory by someone who also has never run a business and never run a state," Romney said.
"Our president has divided the nation, engaged in class warfare and attacked the free-enterprise system that has made America the economic envy of the world. We cannot defeat the president with a candidate who has joined that very assault on free enterprise," he said, adding, "Those who pick up the weapons of the left today will them turned against us tomorrow."
Pelting rain kept voting lines short throughout the day, possibly cutting turnout, observers said.
Romney's fortunes had faded in the Palmetto State in recent days, with news his initial razor-thin win in the Iowa caucuses is now considered a tie with Santorum and Gingrich making headway in South Carolina by painting Romney as a "Massachusetts moderate."
Gingrich's strong performance in Thursday's debate in Charleston, which included a strong defense against accusations by an ex-wife, helped boost his numbers.
Former Alaska Gov. Sarah Palin, the 2008 GOP vice presidential nominee, called on South Carolina voters to choose Gingrich as the conservative alternative to Romney and keep the primary contest alive.
Romney won the New Hampshire primary earlier this month, and Gingrich's win Saturday marks three different results in the first three contests.
The campaign moves to Florida next, where voters have been casting early ballots in advance of the Jan. 31 primary.