Man-of-the-match Thilan Samaraweera earlier cracked a solid 104 under pressure for his maiden one-day century to help Sri Lanka post a competitive total before Malinga completed the victory under lights.
Malinga bowled opener Brendon McCullum with the second ball of his fourth over, had Jacob Oram caught behind and then bowled Nathan McCullum with the last two deliveries to send the tourists reeling at 41-6.
Grant Elliott top-scored with 41. Ian Butler (25), McCullum (14) and skipper Daniel Vettori (10) were the other batsmen to reach double-figures in a dismal batting performance.
The hosts put New Zealand under pressure when they grabbed three wickets in the opening five overs, with Nuwan Kulasekara taking two in one over and Thilan Thushara one.
Thushara was the first to strike when he trapped Jesse Ryder leg-before in his opening over. Kulasekara had Martin Guptill caught behind and then dismissed Ross Taylor in his third over.
India are the third team in the competition. Each side will play two league matches before the top two qualify for the final on September 14.
Sri Lanka were struggling at 69-5 after electing to bat before Samaraweera led the fightback with a vital 127-run stand for the sixth wicket with Angelo Mathews (51).
Samaraweera, 32, smashed 10 fours in his 124-ball knock to become the oldest Sri Lankan to score a maiden one-day hundred, while Mathews hit four boundaries in his second half-century.
New Zealand paceman Shane Bond marked his return to one-day cricket with an impressive 3-43 performance off 10 overs.
The fast bowler, who played his last one-day international in April 2007, denied Sri Lanka a sound start with two wickets in his opening five-over spell.
Bond, who became eligible to play after severing links with the unauthorised Indian Cricket League (ICL), struck in his first over when he had former captain Mahela Jayawardene caught by Taylor in the slips.
Bond then dismissed hard-hitting opener Sanath Jayasuriya (seven) to reduce the hosts to 22-3. He conceded just nine runs in his opening five overs.
Sri Lanka suffered a setback in the opening over when in-form Tillakaratne Dilshan inside-edged a Daryl Tuffey delivery on to his stumps after contributing just four runs.
Tuffey, who also snapped links with the ICL, finished with 1-35 off nine overs in his first one-dayer in more than two years.
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