Sen. John McCain won the South Carolina primary Saturday night, gaining ground in an unpredictable battle for the Republican presidential nomination. Democrats Hillary Rodham Clinton and Barack Obama split the spoils in Nevada caucuses marred by late charges of dirty politics. Clinton captured the popular vote Saturday, but Obama edged her out for national convention delegates at stake, taking 13 to her 12. McCain called his victory in the South Carolina primary evidence that his campaign "can carry right through" Florida into the giant round of caucuses and primaries on February 5. "I know it's not easy," he told The Associated Press, "and we've got a long way to go." The Arizona senator defeated former Arkansas Gov. Mike Huckabee in a close race in the conservative state that snuffed out his presidential hopes eight years ago, when George W. Bush won there. McCain was gaining 33 percent of the vote to just under 30 percent for his closest rival. "It just took us a while. That's all. Eight years is not a long time," McCain told the AP. Appearing before supporters, Huckabee was a gracious loser, congratulating McCain for "running a civil and a good and a decent campaign." Far from conceding defeat in the race, he added, "The process is far, far from over." Former Tennessee Sen. Fred Thompson was in a struggle for third place with about 16 percent, after saying he needed a strong showing to sustain his candidacy. Another Republican, California Rep. Duncan Hunter, dropped out even before the votes were tallied. Candidates from both parties are looking to gain the edge in the runup to Super Tuesday, February 5, when two dozen states cast what could be deciding votes for the presidential nominees. Candidates are vying to amass enough delegates in state-by-state contests to secure their party's presidential nomination at the national convention this summer. With three contests on the ballot, Saturday was the busiest day of the presidential campaign to date, and fittingly enough for a pair of wide-open races, every contest produced a different winner. Former Massachusetts Gov. Mitt Romney rolled to victory in Nevada Republican caucuses, winning roughly 50 percent of the vote in a multi-candidate field. With a black man and a woman as the leading contenders, the Democratic race was history in the making - and increasingly testy, as well. Obama, who won the kickoff Iowa caucuses less than a month ago, issued a statement that said he had conducted an "honest, uplifting campaign ... that appealed to people's hopes instead of their fears." His campaign manager, David Plouffe, was far more pointed in a written statement that accused the Clinton campaign of "an entire week's worth of false, divisive attacks designed to mislead caucus-goers and discredit the caucus itself." Interviews with Democratic caucus-goers indicated that Clinton won about half the votes cast by whites and women, and two-thirds support from Hispanics, many of them members of the union that endorsed Obama. He won about 80 percent of the black vote. Obama and Clinton face off again in next Saturday's primary in South Carolina in their historic Democratic race. The state is home to thousands of black voters, who are expected to comprise as much as half the Democratic electorate. On the Republican side, Romney's western victory marked his second straight success, coming quickly after a first-place finish in the Michigan primary revived a faltering campaign. Romney had campaigned for months to win early contests in Iowa and New Hampshire, and his candidacy was in trouble when he lost both. Nevada Republicans said the economy and illegal immigration were their top concerns, according to a survey of voters entering the caucuses. Romney led among voters who cited both issues. Nearly complete returns showed him winning more than 50 percent of the vote, with libertarian-leaning Texas Rep. Ron Paul and McCain far behind vying for second. Thompson, the former "Law & Order" TV actor, and Huckabee trailed. Romney said Republicans had cast their votes for change - and that he was the man to provide it. Mormons gave Romney about half his votes. He is hoping to become the first member of his faith to win the White House. Romney also won at least 17 of the 31 Republican National Convention delegates at stake. McCain and Paul won at least four apiece, while Thompson and Huckabee each won two. Rudy Giuliani won one delegate - the first of the campaign for the former New York mayor. Alone among the major Republican contenders, Giuliani skipped the day's events. He camped out in Florida, the first of the big states to vote, with a winner-take-all primary. Most of the Republican contenders focused Saturday on the contest in South Carolina, a primary that has gone to the party's eventual nominee every four years since 1980 when Ronald Reagan won the White House. The economy and immigration were cited as top issues, with more than half the voters saying illegal immigrants should be deported. Conservatives and white evangelical voters turned out in heavy numbers, according to the polling place interviews. McCain, a former Vietnam prisoner of war, appealed to a large population of military veterans in South Carolina, and stressed his determination to rein in federal spending. Huckabee, an ordained Baptist minister, reached out to evangelical Christian voters, hoping to rebound from a string of disappointing showings since his victory in the January 3 Iowa caucuses with strong support from religious voters. Thompson, a former Tennessee senator, has staked his candidacy on making a strong showing in the first race in his native South. Romney campaigned on a pledge to help restore South Carolina's economy, much as he did in winning Michigan. South Carolina's unemployment rate hit 6.6 percent in December after the largest one-month increase in nearly 20 years.