Rep. Jim DeMint (search) overcame relative obscurity statewide and overwhelmingly beat ex-Gov. David Beasley (search) on Tuesday for the Republican U.S. Senate nomination.

DeMint, a three-term congressman from Greenville, told The Associated Press that voters selected him because he has "specific solutions for the problems we're facing."

Voters who returned the polls picked DeMint 59 percent to 41 percent over Beasley in unofficial results with 97 percent of the precincts reporting. DeMint led 147,807 votes to Beasley's 102,782.

DeMint, who's spent about $3.5 million so far, will face Democratic state Education Superintendent Inez Tenenbaum (search) this fall for the seat being vacated by retiring Sen. Ernest "Fritz" Hollings (search), a Democrat who has held his seat for nearly 40 years.

Beasley was unable to shake the past in which he was questioned about exaggerations and fluctuating opinions. In 1998, he was ousted from the governor's office after one term during which he changed his mind about the Confederate flag and called for its removal from atop the Statehouse.

Beasley and DeMint had been in a fierce battle since they emerged from the six-way June 8 primary as the top vote-getters. Beasley actually finished that race with the most votes, but since neither got more than 50 percent, a runoff was scheduled.

The two generally sparred over trade issues and how best to revive South Carolina's manufacturing-heavy economy. DeMint supports free trade, while Beasley is more of a protectionist.

"We have to move forward in an international economy," DeMint said Tuesday night.

Beasley called DeMint shortly before 9 p.m. to concede and congratulate him.

"We fought hard. We did what was good. We did what was right," Beasley later told supporters. "All of that which we stand for is bigger than David Beasley, is bigger than Jim DeMint."

Political observers said voter turnout was the key, especially in the Lowcountry, which was up for grabs. The two former GOP Senate candidates from that area endorsed DeMint, who is from Greenville.

Turnout was mixed across the state. In areas such as Charleston and Spartanburg counties where local races also were on the ballot, voters formed short lines throughout the day. Other areas reported typically low runoff turnout.