LAS VEGAS -- Sen. Hillary Rodham Clinton, capturing significant support from Latino voters, won a tough battle in Nevada's caucuses yesterday, as she jumped ahead of Illinois Sen. Barack Obama in the fiercely competitive contest for the Democratic presidential nomination.

In the Republican race, former Massachusetts Gov. Mitt Romney, the only GOP candidate to campaign significantly here, won easily.

Mrs. Clinton took nearly 51 percent of the vote in her party's caucuses, while Mr. Obama received 45 percent. Former North Carolina Sen. John Edwards was in a distant third, receiving less than 4 percent.

"We will build on what we achieved here today," Mrs. Clinton told a crowd of supporters. "We're the problem solvers. We have the answer for what to do to keep this country strong and move with confidence and optimism into the future."

The Silver State saw a record turnout among Democrats, with more than 114,000 voters showing up at more than 1,700 sites across the state, exceeding even the highest estimates put forward by party officials in recent days.

It was more than 10 times the number taking part in 2004, when Nevada's spot on the primary calendar came later and had little influence.

Mrs. Clinton's victory broke a tie from the first two contests of 2008. She defeated Mr. Obama in New Hampshire this month; he was the victor in the Iowa caucuses.

Nevada was given a coveted early spot on this year's electoral calendar as national party leaders sought to include a state with large urban areas and more diversity than mostly rural and white Iowa and New Hampshire. (One out of every four Nevadans is Hispanic.)

Interviews with Democratic caucus-goers indicated that Mrs. Clinton fashioned her victory by winning about half the votes cast by whites, and two-thirds of those from Hispanics, according to The Associated Press. Mr. Obama won about 80 percent of the black vote.

Mrs. Clinton routed him in Clark County, home to Las Vegas, the state's population center and one of the fastest growing cities in the U.S.

It was a major disappointment for the Illinois senator, who had the backing of the 60,000-member Culinary 226, the state's largest union.

Many of its members work in the massive casinos that line the Las Vegas Strip. The Democratic Party set up nine unusual "at-large" caucus sites along the Strip to accommodate eligible voters who were working yesterday.

Yet turnout at Strip caucuses wasn't heavy, and many Culinary union members caucused for Mrs. Clinton.

"I like her. She wants to bring the troops back," said Maria Bravo, 56, a porter at the Riviera Hotel and Casino, referring to the former first lady's promise to start withdrawing from Iraq. (Mr. Obama, too, wants to withdraw troops.)

Ms. Bravo was at Wynn Las Vegas, one of the city's fanciest resorts. She was one of 397 people who attended the at-large caucus in a cavernous meeting room that usually costs $10,000 to $15,000 for a day's use. The hotel donated the space to the Democratic Party, according to Peter Early, vice president of human resources.

The 5-million-square-foot hotel and casino has 9,300 employees. About 225 expressed interest in attending the caucus. Others came from nearby casinos.

The caucus quickly turned into a rowdy event, as cooks, cleaners, card dealers, waitresses and maintenance workers chanted and yelled at each other across the room. A dozen television cameras filmed their every move.

Obama backers wore red Culinary 226 shirts, while Clinton backers waved a sign with the slogan, "I support my union. I support Hillary."

It was a reminder of recent complaints from the Clinton camp that some union members were feeling pressure to support Mr. Obama.

The at-large caucuses had become a source of bitterness for both campaigns after the Nevada State Education Association unsuccessfully sued to block them from taking place. Culinary 226 leaders accused some Clinton supporters in the education association of trying to disenfranchise Latino and black workers on the Strip.

"Hillary Clinton doesn't respect our people," said a Spanish-language radio advertisement that played repeatedly in the days leading up to the vote. It was paid for by Unite Here, Culinary 226's parent organization.

Yet, at the Wynn, Latinos were overwhelmingly enthusiastic about Mrs. Clinton, giving her a narrow two-vote victory after the second round of caucusing.

Some Strip workers who came to the event had little interest in politics.

"We just wanted to see what's going on," said Lisa Escobar, 29, a waitress who had finished an overnight shift at Wynn's Tryst nightclub.

"It's pretty cool, man" said Matt Lopez, 25, a card dealer at Circus Circus. "I've never voted in a caucus before."

He backed Mr. Obama, saying, "He just seems less tainted than the other candidates."

Mr. Obama now likely faces a must-win scenario in his party's South Carolina primary on Jan. 26. Polls give him an edge there, and he is hoping for strong support from black voters, who make up as much as half of Democratic voters in the state.

A South Carolina victory could give him a boost going into "Super Tuesday," Feb. 5, when 22 states vote. But he already faces a disadvantage. Some of those states, including California, have sizeable Latino populations that lean toward Mrs. Clinton.

Although Mrs. Clinton was backed by more people attending the caucuses than Mr. Obama, Mr. Obama won 13 delegates to her 12 because of the proportional manner in which Nevada awards delegates. In most areas of the state where Mrs. Clinton got the most votes, the party awarded an even number of delegates, so Mr. Obama and she split them evenly. In some rural areas where Mr. Obama did better, the party awarded an odd number of delegates, allowing Obama to wind up with the additional delegate.