Muralitharan captured four for 25 and Mendis claimed two for 24 to bundle the Black Caps out to take Sri Lanka to the top of the group with nine points but their final position will be determined only after Saturday's match between Australia and Pakistan.
New Zealand stand-in captain Ross Taylor top-scored with 33 whereas no other Kiwi batsmen could make more than 20.
Earlier, captain Kumar Sangakkara hit a brilliant century to help Sri Lanka set a modest target of 266 runs for New Zealand after electing to bat first.
They made 265 for nine in their 50 overs with the help of a 145-run partnership for the third wicket between Sangakkara and Mahela Jayawardene, which pulled the team out of early trouble.
Sangakkara made 111 off 128 balls with twelve fours and two sixes while Jayawardene hit 66 with six boundaries.
