CHARLESTON, South Carolina (CNN) -- Arizona Sen. John McCain claimed a significant victory in South Carolina's Republican primary Saturday, coming out on top in the state where his first bid for the White House foundered in 2000.
John McCain celebrates with supporters in Charleston, South Carolina.
"It took us a while, but what's eight years among friends?" McCain said, referring to his loss to George W. Bush in the state's 2000 primary.
McCain edged out former Arkansas Gov. Mike Huckabee.
"The path to the White House is not ending here tonight," Huckabee said after the results came in. "Tomorrow we wake up to fight the battle yet again and yet again." Watch Huckabee pump up supporters »
Former Tennessee Sen. Fred Thompson was in third, followed by former Massachusetts Gov. Mitt Romney. See what the results mean »
McCain ran strong in the coastal Low Country around Charleston and ran even with Huckabee in the state's inland Piedmont region, according to exit polls.
"It is an impressive victory. It was a narrow victory. What was remarkable is he did it without carrying conservatives. South Carolina is the homeland of conservatives. That's why it exercises so much influence in the Republican Party," said CNN senior political analyst Bill Schneider. Watch our political team analyze the day »
"Essentially, McCain did it on a personal vote. It wasn't ideology; it wasn't issues. It was a vote for him personally, which has always been his strongest appeal," Schneider said. Watch McCain thank supporters in South Carolina »
The state's Republican primary voters have picked their party's eventual nominee in every election since 1980.
South Carolina's Democratic primary is next Saturday.
The Republican results came in just hours after Nevada held its caucuses. See scenes from Saturday's races »
On the Democratic side, Sen. Hillary Clinton took Nevada, and among Republicans, Romney was the winner.
Clinton led rival Barack Obama by 6 percentage points with 98 percent of precincts reporting.
Although Clinton won the overall state vote, Obama took more delegates because of the areas where he won. CNN projects that Obama will pick up 13 delegates to Clinton's 12.
Former North Carolina Sen. John Edwards was a distant third.
California Rep. Duncan Hunter, who received just 2 percent of the GOP vote, abandoned his presidential bid after the results came in.
Former New York Mayor Rudy Giuliani, who had poor showings in both Nevada and South Carolina, largely skipped the early voting states to focus on Florida and the delegate-rich states competing in the Super Tuesday contests on February 5.
In both South Carolina and Nevada, Republicans named the economy as the most important issue affecting their vote in the primary and caucus, according to early exit polling data.
And illegal immigration was the second-most important issue. The war in Iraq, followed by terrorism, were next, the exit polls showed.
Exit polls in South Carolina indicated clear divisions among voters. Among those who considered themselves born-again or evangelical Christians, Huckabee won a clear victory.
Among those that viewed the war in Iraq to be the most important issue, McCain was dominant -- but Iraq ranked as only the third-most important issue among all voters.
McCain tried unsuccessfully to extend polling hours in South Carolina after learning voting machines in the eastern part of the state were malfunctioning, according to a lawyer for his campaign.
Earlier in the day, Clinton thanked her supporters in Nevada.
"I guess this is how the West was won," she said. Watch Clinton celebrate in Nevada »
Clinton issued a special thanks to her supporters from the 60,000-strong Culinary Workers Union. Clinton had been encouraging members of the union, which endorsed Obama, to vote their conscience.
Zachary Conine, a permanent caucus chairman in Las Vegas, said Clinton's campaign organization helped hand her the win.
"Her people are efficient, fervent. They were there first, they were calling people, they had a list of voters they were using to call people, making sure people came out. They had signs, they had shirts, they had a clear chain of command," he said.
Nevada marks the third win for Romney. He took Michigan on Tuesday and also won the overshadowed contest in Wyoming.
"If you can win those two states -- Michigan and Nevada -- it means you have put together quite a coalition and have been able to make the kind of inroads you have to make to take the White House," he said Saturday afternoon from Florida. Watch Romney claim victory »
In a presidential race that's increasingly coming down to who has the most delegates, a win helps Romney.
Romney also benefited from his Mormon religion, the poll results show. Romney captured 94 percent of the voters who identified themselves as Mormon, which made up 25 percent of all Republicans participating in the GOP caucuses.
The Church of Jesus Christ of Latter-day Saints estimates there are 170,000 members living in Nevada.
So far among Democrats, Clinton has won New Hampshire, Nevada and Michigan. In Michigan, she was the only major candidate on the ballot. Obama claimed victory in Iowa.
Among Republicans, Huckabee won Iowa, McCain won New Hampshire and South Carolina, and Romney won Wyoming, Michigan and Nevada.
The Democrats next face off in South Carolina on Saturday, and the Republican race heads to Florida for the January 29 primary. E-mail to a friend
CNN's Bill Schneider and Kate Taylor contributed to this report.