MIAMI, Florida (CNN) -- Drawing heavily on votes from senior citizens, Hispanics and moderates, Arizona Sen. John McCain won Tuesday in Florida, the biggest prize thus far in the race for the Republican presidential nomination.
But exit polling by CNN suggests that McCain scored points in areas he wasn't expected to. He outpaced chief rival Mitt Romney, the former Massachusetts governor who campaigned as a successful businessman, among voters who cited the economy as their chief concern.
And while losing to Romney among self-described conservatives, McCain stayed close -- allowing more moderate votes in south Florida and support in the state's military communities to push him over the top.
With 73 percent of precincts reporting, McCain had 36 percent of the vote, compared to 31 percent for Romney.
"Florida has always been a special place to me, and it is even more so tonight," McCain said to supporters. "Our victory might not have reached landslide proportions, but it is sweet nonetheless."
The results also dealt a seemingly crushing blow to the hopes of former New York Mayor Rudy Giuliani -- who had staked his entire campaign on a win in Florida only to end up struggling to finish third.
Florida has 57 delegates to the GOP nominating convention -- making it by far the largest state yet to vote. It is also a "winner take all" state, meaning that all of those delegates will be going to McCain, not split based on the percentage each candidate earns. Watch scenes from the 2008 battle for the White House »
Exit polling of 1,505 Republican voters showed that McCain, who will be 72 when the Republicans hold their convention in September, won big with older voters -- who make up a sizable portion of Florida voters.
Voters 65 and older represented 33 percent of the GOP electorate -- and 38 percent of those voters picked McCain, according to the polls. Thirty-one percent supported Romney.
The economy was the top concern among voters -- and McCain took the majority of those votes as well, despite Romney's efforts to promote himself as a business leader best suited to help jump-start a flagging economy.
Thirty-eight percent of voters who said they were most concerned about the economy voted for the Arizona senator, compared to 32 percent for Romney.
Early exit polls on Tuesday suggest that many of the moderate voters Giuliani -- a big city mayor whose views on issues like abortion and immigration haven't always jibed with more conservative voters -- were flocking to McCain.
Forty-one percent of Florida voters who described themselves as moderates said they voted for McCain, compared to 22 percent for Giuliani.
Romney was looking to more conservative voters for the lion's share of his support.
Among the 1,505 poll respondents, 37 percent of those who called themselves conservative went for Romney. But McCain was only 10 points back at 27 percent. McCain was hoping to stay close enough to Romney among evangelicals and other conservatives to use his bigger lead among moderates for a win.
Moderates only made up 28 percent of the poll respondents, but McCain held an 18-point advantage over Romney among them.
Analysts noted that McCain -- whose reputation as a maverick put him at odds with many diehard Republicans during his 2000 campaign against President Bush -- is yet to be the favorite among self-styled conservatives in any contest this season.
CNN political analyst Bill Bennett, who hosts a conservative radio talk show, said McCain will need to reach out to that wing of the party to maintain his front-runner status and shore up support in the general election if he wins the nomination.
"He is likely on his way to the nomination, but he has got to mend his fences with conservatives, because you do not want a convention with a lot of unhappy people," Bennett said.
"The anger and bitterness at John McCain is extreme among a lot of conservatives."
That effort appeared to have begun during McCain's acceptance speech Tuesday night.
He sounded popular conservative themes, including a promise to appoint conservative judges to the federal bench, and cited Republican icon Ronald Reagan as his inspiration for first becoming a Republican.
"I am as proud today to be a Republican conservative as I was then," he said.
Members of Florida's influential Hispanic community appear to have gone largely for McCain, according to polling.
Half of those who described themselves as Cuban voted for McCain -- compared to only 10 percent for Romney -- and non-Cuban Hispanics who were polled voted 51 percent for McCain versus 21 percent for Romney.
Hispanic voters accounted for 10 percent of the vote in the GOP primary.
McCain also appeared to be buoyed by the endorsement last week of Florida Gov. Charlie Crist.
While voters tend to discount the importance of endorsements by newspapers and other politicians, 42 percent of poll respondents said that the nod from Crist was important to their decision. Of those respondents, more than half -- 52 percent -- said they voted for McCain. E-mail to a friend
CNN's Bill Schneider, Paul Steinhauser and Alexander Mooney contributed to this report.
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