By Michele Kambas and Deepa Babington

NICOSIA (Reuters) - Cypriot conservative leader Nicos Anastasiades won an overwhelming victory in a presidential run-off election on Sunday, boosting hopes of a swift financial rescue for the near-bankrupt island nation.

Tiny Cyprus has emerged as a big headache for the euro zone in recent months, triggering fears the island could plunge into a financial meltdown that reignites the bloc's debt crisis. A bailout has proved elusive eight months since talks began.

Anastasiades, who has pledged to hammer out a quick deal with foreign lenders, took 57.5 percent of the vote, 15 points ahead of his Communist-backed rival Stavros Malas, who campaigned on an anti-austerity platform.

Jubilant supporters waved Greek and Cypriot flags, honked car horns and set off flares in Nicosia as the results came in.

"It's a triumph," said Stefanos Stefanou, a 62-year-old pensioner as he stood outside Anastasiades's campaign offices. "I won't have the fear of losing my pension and benefits now, along with what we earned after working for 40 years."

Financial markets had been hoping for an Anastasiades victory to speed up a joint rescue by the European Union and International Monetary Fund before the island runs out of cash and derails fragile confidence returning to the euro zone.

"We need a government with weight that can talk to (EU) partners, that is cooperative, that can be heard and do what it pledges to do," Christopher Pissarides, a Cypriot who won the Nobel prize in economics in 2010 told Reuters.

"We hadn't been doing this until now. The most important thing is to signal our willingness to cooperate (with the EU)."

WELL VERSED ON RULES

Anastasiades will take the reins of a Mediterranean nation ravaged by its worst economic crisis in four decades, with unemployment at a record high of 15 percent. Pay cuts and tax hikes ahead of a bailout have further soured the national mood.

"I would expect the markets, and business, to welcome Anastasiades's victory because he knows the rules of the game very well," said Stelios Platis, an economist and independent consultant. "Securing funding for the state is the immediate priority, along with signing the bailout agreement."

Turnout was lower than expected among the half a million Cypriots eligible to vote, with a high 19 percent abstention rate blamed on despondency at the country's grim prospects.

Talks to rescue Nicosia have dragged on eight months since it first sought help, after a Greek sovereign debt restructuring saddled its banks with losses. It is expected to need up to 17 billion euros in aid - about the size of its entire economy.

Anastasiades has suggested the island may even need a bridging loan to tide it over until a rescue is nailed down.

Virtually all rescue options - from a bailout loan to a debt writedown or slapping losses on bank depositors - are proving unpalatable because they push Cypriot debt to unmanageable levels or risk hurting investor sentiment elsewhere in the bloc.

German misgivings about the nation's commitment to fighting money-laundering and strong financial ties with Russia have further complicated the negotiations.

European officials want a bailout agreed by the end of March, ensuring no honeymoon period for the new president, who will be sworn in on February 28 and assume power on March 1.

Longstanding anger over the island's 40-year-old division into the Greek-speaking south and Turkish north has been relegated to a distant second behind the country's financial quagmire as an election issue this year.

A heavy smoker known for his no-nonsense style, Anastasiades is widely respected but suffered political humiliation nine years ago when he supported an unpopular U.N. blueprint to reunify the island that was later rejected by the public.

(Additional reporting by Stelios Orphanides; Writing by Deepa Babington; Editing by Will Waterman)