The Kiwis, shot out for 188, hit back to remove swashbuckling opener Sanath Jayasuriya first ball and Marvan Atapattu and Aravinda De Silva by the fourth over to make it 5-3.
Ranatunga and opener Romesh Kaluwitharana however saw off the unexpected crisis with a 127-run partnership for the fifth wicket as Sri Lanka cruised home with more than eight overs to spare.
Kaluwitharana was run out in the 30th over for 48 and the recalled Roshan Mahanama departed for seven, but the unflappable Ranatunga held his end up till victory was achieved.
New Zealand paceman Simon Doull gave Sri Lanka a scare when he had Jayasuriya caught superbly off the inside edge by wicket-keeper Adam Parore with his first delivery.
Parore, who top-scored with 54 in New Zealand's dismal innings, helped himself to another catch when Atapattu edged a wild shot in Doull's second over.
What should have been a cakewalk for Sri Lanka turned into a nightmare in the fourth over when De Silva edged a drive off Geoff Allott to second slip where Nathan Astle gleefully accepted the low catch.
Ranatunga and Kaluwitharana however wrested the initiative to deny New Zealand another upset after their thrilling last-ball win over Zimbabwe in Saturday's opener.
Sri Lanka now clash with South Africa on Friday for a place in the final of the limited-overs tournament featuring the nine Test-playing nations.
Ranatunga attributed the early collapse to lack of practice at home because of bad weather.
"We are a bit out of touch at the moment, but we have three days now to discover our form before the semi-final," he said. "We should try and take advantage of the good batting conditions here."
Sri Lanka's win was set up by off-spinner Muttiah Murlitharan who sliced through New Zealand's batting to bowl them out for 188 in the first session.
The versatile spinner, playing for the first time since his 16-wicket haul in the Oval Test against England in August, finished with 3-31 in 10 deadly overs.
Murlitharan struck in his first over, having Matthew Bell stumped. He then bowled Alex Tait and finished his quota of 10 overs by having Daniel Vettori caught behind.
The Kiwis found Sri Lanka's steady attack too hot to handle and folded up with a ball to spare after three batsmen were run out and the last six failed to get into double figures.
Left-arm seamer Chaminda Vaas, who missed the English tour because of injury, marked his return to international cricket with 1-27 from seven steady overs.
Jayasuriya began New Zealand's downfall with a superb diving catch at point in the fourth over as Nathan Astle slashed at lanky left-arm seamer Nuwan Zoysa. Skipper Stephen Fleming and Bell carried the score to 56 when both batsmen fell in the space of two overs to make the Kiwis 58-3 in the 15th over. Parore and Craig McMillan (26) boosted the score with a 60-run partnership for the fourth wicket, before McMillan was run out by a superb throw from Upul Chandana.
Chris Harris, whose last-ball boundary caused Zimbabwe's defeat on Saturday, made only eight when he was caught in front of the wicket by Jayasuriya.
Parore, frustrated at little support at the other end, departed in
the 43rd over when he holed out to long-on against Kumara Dharmasena.
Date-stamped : 26 Oct1998 - 15:41