DETROIT — Mitt Romney scored his first major primary victory today in his native Michigan, a win he desperately needed to give his weakened candidacy new life and set the stage for a wide-open Republican showdown in South Carolina in just four days.

Mr. Romney was the third Republican victor in the first four states to vote in the 2008 primary season, further roiling a volatile nomination fight that lacks a clear favorite.

The former Massachusetts governor defeated Senator McCain, the Arizona senator who was hoping that independents and Democrats would join Republicans to help him repeat his 2000 triumph here. Michael Huckabee, the former Arkansas governor, trailed in third, and a former Tennessee senator, Fred Thompson, was waiting for the top three candidates in South Carolina, already campaigning.

“It’s a victory of optimism over Washington-style pessimism,” Mr. Romney said, echoing his campaign speeches. “Now on to South Carolina, Nevada, Florida.”

Mr. McCain said he had called Mr. Romney to congratulate him “that Michigan welcomed their native son with their support.”

“Starting tomorrow, we’re going to win South Carolina, and we’re going to go on and win the nomination,” Mr. McCain declared.

Mr. Romney’s ties to Michigan proved beneficial.

Four in 10 voters said his roots factored into their votes, and more than half of that group backed Mr. Romney, according to preliminary results from surveys of voters as they left their polling places, taken for The Associated Press and the networks. He also led among voters who said the economy and illegal immigration were their most important issues, and won a majority of Republicans, conservatives, and voters looking for a candidate with experience.

Mr. McCain had an edge with those who wanted an authentic president, and he won among moderates, independents and Democrats. But fewer non-Republican voters participated in the Republican primary this year than in 2000 when those voters helped him beat George W. Bush. Independents and Democrats accounted for roughly one-third of the vote, compared with about one half eight years ago.

Mr. Romney had a slight edge over Mr. McCain as the candidate likeliest to bring needed change.

The economy proved the most important issue for Republicans in Michigan, the state with the highest unemployment rate in the nation and an ailing auto industry. Given four choices, half of Michigan Republican primary voters picked the economy as the most important issue, while one in five picked Iraq, one in seven immigration and one in 10 terrorism.

A mere 20% of eligible voters were expected to show up at polling stations across frigid and snowy Michigan; turnout was likely to be depressed by a Democratic race of little to no consequence.

Senator Clinton was the only top contender on the Democratic ballot.

For Republicans, the stakes varied.

Of the three candidates competing hard here, Mr. Romney needed a Michigan victory the most to invigorate a campaign weakened by searing losses in Iowa and New Hampshire. He was the only one watching the voting returns in Michigan; his top Michigan opponents, Messrs. McCain and Huckabee, campaigned in the state earlier in the day but left by afternoon to plant themselves in South Carolina, which votes Saturday.

Up for grabs in Michigan were 30 Republican delegates.

Mr. Romney, who has put at least $20 million of his personal fortune into his bid, campaigned in the state far more than his rivals and spent more than $2 million in TV ads in Michigan, nearly three times what Mr. McCain did, according to an analysis of presidential advertising by the nonpartisan Michigan Campaign Finance Network. Mr. McCain paid for more than $740,00 in ads and Mr. Huckabee spent more than $480,000.

A muddle from the start, the Republican race has grown ever more fluid as the first states voted over the past two weeks.

Mr. Huckabee won the Iowa caucuses, Mr. McCain prevailed in New Hampshire’s primary, and Mr. Romney was second to both — but claimed victory in scarcely contested Wyoming. A former Tennessee senator, Fred Thompson, is camping out in South Carolina looking for his first win. Mayor Giuliani is doing the same in Florida, which votes January 29.

Mr. Romney was born and raised in Michigan, and his late father, George, was head of American Motors and a three-term governor in the 1960s. Mr. Romney announced his presidential candidacy in Michigan a year ago, campaigned in it far more than his rivals and spent considerably more money on advertising.

Mr. McCain had a built-in advantage of his own. He won the state’s primary eight years ago on the strength of independent and Democratic-crossover voters, and he still had a network of hard-core backers. This year, Mr. McCain didn’t have to compete full-bore for non-Republican voters because the Democratic race in Michigan was essentially a beauty contest. Six months after his campaign nearly collapsed, he now leads national polls.

Mr. Huckabee, an ordained Southern Baptist minister, hoped to stage a surprise finish with the support of Christian evangelicals who live in the more conservative, western part of the state. With his populist pitch, Mr. Huckabee also wanted to do well in Reagan Republican country outside of Detroit. He came from behind to win the Iowa caucuses and sought another surprise finish in Michigan.

The economy dominated the weeklong Michigan campaign. The state has been reeling from the auto industry’s downturn and has the nation’s highest unemployment rate at 7.4%.

Michigan doesn’t typically hold its primary until February but state party officials scheduled it earlier to try to give the state more say in picking a president. The Republican National Committee objected and cut the number of Michigan delegates to the national convention by half as punishment while the Democratic National Committee stripped the state of all 156 delegates to its national convention, including 28 superdelegates who would not have been bound by the outcome of the primary.