Muralitharan finished with six for 87 to claim an impressive ninth five-wicket haul for the year, as Sri Lanka wrapped up the Test with four sessions to spare.
They had set New Zealand the improbable target of 504, but the home side had never batted with authority in the series and the outcome always seemed inevitable.
Despite a defiant eighth wicket stand by Daniel Vettori and James Franklin who put on 96, New Zealand were unable to cope with Muralitharan's mesmerising spin backed by Lasith Malinga's slingshot speed.
Their second innings ended at 286 shortly before the scheduled tea break on the fourth day.
But while the New Zealand batsmen failed to fire, Vettori providing their only half century, captain Stephen Fleming said full credit had to go to Sri Lanka's spectacular attack.
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"The unorthodox nature of their attack was always going to pose a problem -- one of the greatest bowlers of all time and an action that's very hard to pick up makes it tough," he said.
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