The ace spinner was irresistible on a wicket held together with synthetic adhesive, but New Zealand produced a disappointing batting performance.
Nathan Astle hit 42 before sweeping Muralitharan to deep square leg, but the rest of the top seven all failed.
Daniel Vettori's 46 not out at the death gave them something to defend.
He put on 47 for the final with with Jeetan Patel, easily the best partnership of the innings.
Finding lavish swing with the new ball, Chaminda Vaas removed Stephen Fleming lbw for 13 in the fifth over of the match to get the ball rolling for the Sri Lankans.
Lou Vincent's misjudged swipe at Farveez Maharoof made it 37-2 before Hamish Marshall cut Lasith Malinga to backward point.
After Sanath Jayasuriya had removed Scott Styris, Murali took his four wickets, the best of the bunch a doosra which bowled Jacob Oram behind his legs.
Jayasuriya snared a second victim to leave New Zealand 118-9 in the 39th over and at that point the match looked hopelessly one-sided.
But Vettori hit three boundaries off as many balls in Vaas' last over, which cost 19, including a deft leg-glance.
Finally, Malinga had Patel caught at point four balls from the end.
Brief Scores: New Zealand 165 all out in 49.2 ( Nathan Astle 42, D Vettori 46; Muralitharan 4 for 23, Jayasuriya 2 for 26, L Malinga 2 for 22)