Ponting was as at his mercurial best to notch his 24th one-day international ton, while Gilchrist, who cracked six fours and two sixes before being dismissed for 51, took the game away from New Zealand, who made 254 for seven off 50 overs.
Ponting also combined with Michael Clarke (48) for a 135-run match-winning partnership after Matthew Hayden (17) and Gilchrist were dismissed in quick succession, though Gilchrist's onslaught had put Australia firmly in control.
Clarke was caught by Lou Vincent off Kyle Mills with just 46 runs needed for victory before Ponting and Andrew Symonds (28 not out) saw Australia home with 7.3 overs to spare.
"Gilchrist was pretty brutal. He had a go and really took the momentum away from us," said New Zealand captain Daniel Vettori.
Wicketkeeper Brendon McCullum and Ross Taylor provided the bulk of New Zealand's runs but both fell at crucial times when trying to increase the scoring rate after being bogged down by tight Australian bowling.
McCullum, promoted to open the batting, anchored New Zealand's innings with 96 -- his highest one-day score -- but was caught by Nathan Bracken in the deep off left-arm spinner Brad Hogg just when it seemed he would push on to three figures.
Taylor, who had been struggling for form, crafted a careful 50, but threw his wicket away when he got a leading edge off Brett Lee and was easily caught by Shaun Tait at wide mid-off.
Tait, who had been smashed for 28 runs in his first three overs, finished with 3-59 off 10 overs.
The next match in the three-match series is on Sunday in Sydney.


SCORE BOARD

NEW ZEALAND
Vincent c Hopes b Lee 5
McCullum c Bracken b Hogg 96
How c Hayden b Tait 20
Styris c Gilchrist b Tait 5
Taylor c Tait b Lee 50
Oram (not out) 32
Sinclair c Hogg b Hopes 2
Vettori b Tait 18
Mills (not out) 7
Extras (B-1, LB-5, NB-5, W-8) 19
Total (for 7 wkts, 50 overs) 254
Fall of wickets: 1-16, 2-155, 3-123, 4-175, 5-197, 6-201, 7-241.
Bowling: Lee 10-0-48-2, Bracken 10-3-52-0, Tait 10-0-59-3, Hopes 10-0-40-1, Hogg 10-1-49-1.

 AUSTRALIA
Hayden c&b Mills 17
Gilchrist c Taylor b Martin 51
Ponting (not out) 107
Clarke c Vincent b Mills 48
Symonds (not out) 28
Extras (W-1, NB-3) 4
Total (for three wkts, 42.3 overs) 255
 Fall of wickets: 1-69, 2-75, 3-210.
Bowling: Mills 10-1-68-2, Mark Gillespie 10-0-72-0, Martin 9-1-52-1, Jacob Oram 4.3-0-25-0, Daniel Vettori 8-0-32-0, Styris 1-0-6-0.