Hillary Rodham Clinton won the Florida Democratic primary Tuesday night, an event that drew no campaigning by any of her presidential rivals and awarded no delegates to the winner. The New York senator, fresh off her lopsided loss to Barack Obama in last weekend's South Carolina primary, arranged a rally in the state as the polls were closing, an evident attempt to gain campaign momentum. She and Obama collide next week in a coast-to-coast competition for delegates in more than 20 states. Last year, the national party stripped Florida of its 185 delegates as punishment for moving its primary ahead of Feb. 5 and the candidates pledged to bypass the state. Still, Clinton winked at that pledge, holding two closed fundraisers in recent days and scheduling a rally with supporters after the polls closed in Florida. It is expected that the eventual nominee will try to seat delegates from Florida and Michigan, reversing the Democratic National Committee's punishment. "I will try to persuade my delegates to seat the delegates from Michigan and Florida," said Clinton. "Democrats have to win Michigan and have to try to win Florida and I intend to do that. The people of Florida deserve to be represented in the process of picking a candidate for president of the United States." Michigan also violated party rules by moving its primary to Jan. 15, and party leaders voted to strip the state of its 156 delegates as punishment. Meanwhile, Sen. John McCain won a breakthrough triumph in the Florida Republican primary, gaining the upper hand in the battle for the presidential nomination ahead of next week's contests in more than 20 states. Former New York Mayor Rudy Giuliani appeared ready to quit the race. "It shows one thing. I'm the conservative leader who can unite the party," McCain said in a brief interview Tuesday night with The Associated Press. "It's a very significant boost, but I think we've got a tough week ahead and a lot of states to come." Returns from 62 percent of the state's precincts showed McCain, the Arizona senator, with 36 percent of the vote and Romney, the former governor of Massachusetts, with 31 percent. The victory solidified McCain's status as the front-runner for the Republican presidential nomination, his candidacy having come full circle in little more than a year when he was lagging in the polls and in fund-raising. The victory was worth 57 national convention delegates for McCain, a winner-take-all haul that catapulted him ahead of Romney for the overall delegate lead. Giuliani ran third, his best showing of the campaign but not nearly good enough for the one-time front-runner who decided to make his last stand in a state that is home to tens of thousands of transplanted New Yorkers. In remarks to supporters in Orlando, he referred to his candidacy repeatedly in the past tense - as though it was over. "We'll stay involved and together we'll make sure that we'll do everything we can to hand our nation off to the next generation better than it was before," he said.