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Australia, chasing 148 to win, wobbled at 26 for two after James Franklin struck twice in his first over.
But an expertly paced stand of 104 between Ponting and Michael Clarke, unbeaten on 49, helped Australia to victory with four balls to spare as they made it two wins out of two following Monday's defeat of Bangladesh.
Earlier, left-arm quick Mitchell Johnson took four wickets as Australia restricted New Zealand to 147 all out.
New Zealand lost openers Brendon McCullum and Jesse Ryder for a duck apiece and collapsed to 21 for five inside six overs before a stand of 71 between Scott Styris (42) and Peter McGlashan (49) revived the innings.
Johnson though finished with fine figures of four for 20 from four overs.
Australia saw Franklin remove Shane Watson and the big-hitting David Warner.
But Ponting, playing some typically stylish shots, steadied the ship and lofted New Zealand captain and left-arm spinner Daniel Vettori for six before meting out the same treatment to all-rounder Styris.
Ponting, one of the world's best batsmen in all forms of the game, went to fifty in 34 balls, including four fours to go with his pair of sixes.
But in sight of victory, he was caught by Jacob Oram off Vettori.
Australia made an ideal start after Vettori won the toss.
Fast bowler Brett Lee had the dangerous McCullum caught behind after the batsman chased a wide ball while Ryder was out to Johnson's second ball, caught at long leg by Peter Siddle off a hook.
The Black Caps, who on Monday beat defending champions India at Lord's, then slumped to six for three when Martin Guptill, one ball after cover-driving Johnson for four, chipped him to Nathan Hauritz at mid-on.
And when all-rounder Oram was run out without facing a ball following good work by Johnson, the Black Caps were 21 for five off five overs.
However, the experienced Styris counter-attacked by lofting Siddle for a superb straight six into the Pavilion and next ball giving himself room to drive the seamer for four.
McGlashan then got in on the act by pulling Siddle for six in front of a sun-drenched crowd.
But the stand was broken when Brisbane-born Stryris, like McCullum before him, chased a delivery which would have been called wide and was caught by wicket-keeper Brad Haddin, off Johnson.
His 42 had come in 28 balls with two sixes and six fours.
McGlashan kept the momentum going with two reverse swept four off Hauritz before falling to the off-spinner one short of his fifty when caught at long-off by David Hussey having faced 35 balls with a six and six fours.
