* Bloomberg wins narrow re-election

* Margin far slimmer than anticipated (Adds Bloomberg quotes, details)

NEW YORK, Nov 4 (Reuters) - New York Mayor Michael Bloomberg, who engineered a change in the city’s term-limits law so he could run again and set a campaign financing record, narrowly won a third term on Tuesday, local media declared.

Bloomberg, who ran as an independent, defeated City Comptroller Bill Thompson, a Democrat, according to The New York Times, the Daily News and NY1 television.

With 99 percent of the votes counted, Bloomberg was ahead 51 to 46 percent.

His margin was far smaller than expected, given polls that showed him as recently as Monday with a double-digit lead and expectations of a large, lopsided victory.

Bloomberg spent more of his own money in pursuit of public office than any other individual in U.S. history, and he vastly outspent his challenger, laying out $13 for every $1 spent by Thompson.

Described by Forbes magazine as the richest man in New York, with a $16 billion fortune, he has spent almost $90 million on his re-election bid and is on track to spend as much as $140 million overall. Thompson spent $7 million.

Bloomberg pledged in a speech to supporters to cut crime further, reduce the city’s carbon emissions, expand mass transit, increase city parkland, improve schools, add affordable housing and jobs and diversify the local economy.

“Conventional wisdom says that historically third terms haven’t been too successful, but we’ve spent the past eight years defying conventional wisdom,” he said, citing the city’s economic resilience following the Sept. 11 attacks and its success at lowering crime rates.

“We’ve proven the experts wrong again and again and again,” Bloomberg said. “We’re going to make the next four years the best yet.”

Official numbers were not yet calculated, but turnout appeared low. Some 4.2 million New Yorkers are registered voters.

Noting Bloomberg’s unexpectedly slim margin of victory, some political observers said New York voters may have been soured by the mayor’s success in getting the city’s term-limits law amended on his behalf.

Others said Bloomberg supporters may have been lulled by his strong polling numbers and did not turn out in large numbers at the polls.

In arguing that he should be allowed to run for a third term, which the city council allowed by amending the law, Bloomberg said his financial acumen was needed to guide New York through hard economic times.

A former partner at Salomon Brothers, he founded Bloomberg LP, a news and financial information company that competes with Thomson Reuters. (Additional reporting by Edith Honan; editing by Anthony Boadle)