Chasing a not-so-impressive New Zealand total of 188 in 50 overs, Ranatunga, the most experienced Sri Lankan batsman, who came at number five with Sri Lanka tottering at three down for five in the fourth over, remained at the crease till the end to help the islanders reach 191 for five with more than eight overs to spare.
The winners will now face South Africa in the first semifinal on October 30.
The Lankans were off to a disastrous start losing their three front-line batsmen - Sanath Jayasuriya (0), Marvan Atapattu (3) and Aravinda de Silva (0).
New Zealand's opening bowler Simon Doull drew first blood dismissing explosive opener, Jayasuriya, for a duck in the very first ball of the innings. The southpaw went on to play forward to an inswinger which got an inside edge, making the Kiwi wicketkeeper Adam Parore fly to grasp an spectacular catch.
One-down Atapattu was out next in a similar fashion when he tried to drive Simon Doull in the third over but missed the line. The ball went into the hands of Parore after kissing the top edge of his bat.
De Silva, the master batsman, followed Atapattu in the next over when he tried to drive left-arm seamer Geoff Allott but edged to Nathan Astle at second slip without opening his account.
The New Zealand success came to an end at that point when Ranatunga joined little Kaluwitharana.
The duo lifted the Lankans from the darkness of the night into a glistening morning with a patient but match-winning 127-run partnership for the fourth wicket.
The pair, who mostly depended on ones and twos to frustrate the Kiwi bowlers, proved why they are the world champions scoring their first fifty from 69 balls. They completed their 100-run partnership in the 22nd over to take the match into the Sri Lanka grip.
The partnership came to a sorry end in the 30th over when Kaluwitharana was run out from a direct throw by Astle from the mid-on region when he tried to take a quick single off Allott.
In his uncharacteristic innings which saw no ambitious shots, Kaluwitharana scored 48 runs off 75 balls, which included only five boundaries. It was very unfortunate for the Lankan opener to miss his ninth ODI fifty for only two runs.
After Kaluwitharana's departure with Sri Lanka firmly placed on 132 for four, Ranatunga added another 18-runs with Mahanama for the fifth wicket before the latter was brilliantly taken by Allott at deep square leg off a Paul Wiseman delivery.
But that did not have any impact on the Sri Lankan World Cup winning captain, who then teamed up with Upul Chandana to take Sri Lanka home without any further damage.
In his 116-ball undefeated stay at the crease, Ranatunga, who was later adjudged player-of-the-match, hammered eight boundaries. The veteran left-hander reached his 47th ODI fifty off 65 balls inclusive of six fours. He is now exactly 40 runs shy from the elite 7000 club having played his 245th ODI match yesterday.
Chandana remained not out on a run-a-ball 22 with the help of four boundaries.
Earlier, put into bat, the Kiwis were bundled out for 188 in 49.5 overs in the face of some controlled spin bowling from the Lankans.
Off spinner Muttiah Muralitharan led the four-man spin attack finishing with three for 31 from his tight 10-over spell. Kumara Dharmasena, left arm spinner Jayasuriya, Chaminda Vaas and Nuwan Zoysa captured one wicket apiece.
For the New Zealanders, middle-order Adam Parore was the most successful batsman scoring a back-to-back fifty.
Parore, who scored 52 against Zimbabwe in the opening match two days before, scored 54 runs off 87 balls while two other middle-orders, Craig McMillan (26) and skipper Stephen Fleming (25), were also notable run-getters.
After the match, the confident Sri Lankan skipper disclosed that he was not at all worried after the early loss of their three top order batsmen.
``We still had Mahanama and Dharmasena to bat and we were never in panic'' said a beaming Ranatunga.
``It's our habit that we like to chase always and we were successful at the end,'' he added.
Ranatunga also praised his bowlers saying,'' They did a splendid job to stop the Kiwis for only 188.''
On the other hand, the New Zealand skipper said that he was not pleased with the batsmen who could not even cross the 200-mark.
``We had a very small score to defend and the Lankans have out-played us,'' said Fleming after the match.
Fleming appreciated the ``fantastic'' Dhaka crowd.
There will be no match today. The tournament will resume tomorrow with the third quarterfinal between India and Australia.