Defeat would have seen the Sri Lankans eliminated for the tournament, but some inspired bowling restricted New Zealand to 165 before they cruised past the total in the 36th over in reply.
With the wicket a spinner's delight Muralithran was in his element taking 4-23, before young opener Upul Tharanga (56) and captain Mahela Jayawardene (48) put on 89 for the second wicket to lay the foundations for victory.
Both batsmen fell in four deliveries from spinner Jeetan Patel, but Kumar Sangakkara and former skipper Marvan Atapattu guided Sri Lanka to an impressive victory.
"We have come back strongly but we can't afford to relax. We have to keep winning," said Jayawardene, whose team has now won 10 of their last 11 matches.
"The key was to keep the runs down and I think the bowlers, especially Murali, did a great job. Chasing around 230 would have been much harder on this wicket so it was nice to keep them to 165."
New Zealand's Stephen Fleming, who equalled Sri Lankan Arjuna Ranatunga's record of 193 one-dayers as captain, blamed the batsmen for the defeat.
"This definitely was not a 165 pitch," said Fleming. "It played much better than before but we lost momentum with the fall of early wickets. We batted very poorly.
Mahela Jayawardene: a captain's
"Having won our first match, we had the luxury of staying in the tournament after a bad match. We need to raise our game against Pakistan."
The Brabourne stadium wicket, which had been criticised for breaking up, continued to assist the spinners despite the International Cricket Council's pitch consultant Andy Atkinson spraying it with a glue, Polyvinvl Acetate, before the start to help bind it for 100 overs.
But after electing to bat New Zealand only had themselves to blame for the sluggish display that saw the first nine wickets fall for just 118.
Only a last wicket stand between Daniel Vettori (46) and Nathan Astle (42) gave the bowlers something to defend.
When batting Sri Lanka went out hard after their total New Zealand fast bowler Shane Bond was hammered for 36 runs in his first four overs.
Sri Lanka take on South Africa in their last league match in Ahmedabad on Tuesday while New Zealand clash with Pakistan a day later in Mohali.
Both Sri Lanka and New Zealand have one win each from two matches.