The Insider-Advantage/Majority Opinion Research poll of 476 registered voters likely to vote in the GOP primary gave Cain 32 percent of the vote, twice the share of Mitt Romney’s 16 percent.
Rick Perry holds 12 percent, making him essentially tied with Romney because the difference is within the 5 percent margin of error.
"In this case, South Carolina is a three-man race," said InsiderAdvantage CEO Matt Towery.
Rounding out the field is Newt Gingrich with 8 percent, Ron Paul and Michele Bachmann each with 6 and Jon Huntsman with 1. Four percent of those surveyed favored someone not listed in the choices, and 15 percent remain undecided.
Cain, a native of Georgia who once headed a pizza chain before becoming a talk-radio host, was the pick of every age group except seniors who prefer Romney, the former Massachusetts governor.
Where Romney appeals to independents, Cain does best with those identifying as Republicans.
Towery's poll Oct. 4 was the first to show Cain edging past Romney to gain the lead nationally as Perry lost ground.
Perry, the governor of Texas, harmed himself with a response to a cable-TV debate question about immigration where he said people who disagreed were heartless. He was defending signing into law in-state tuition discounts for college students who immigrated illegally as young children.
The response was especially stark in Florida where Towery conducted a survey for The Florida Times-Union, also Sunday evening, showing Perry with just 3 percent while Romney and Cain were essentially tied for the lead.
The steady turnover in the GOP lead nationally has led pundits to describe Cain as merely the "flavor of the month."
Towery credits Cain with more staying power.
"I've seen the flavor of the month almost every time. But he is sustaining himself," he said. "I think he's a little more than the flavor of the month."
Unless he stumbles, Cain has sufficient strength in enough states to be a contender as long as his newfound status in the top tier brings cash he'll need to advertise in large states like Florida with multiple media markets, Towery said.