Scorecard
Victory saw Australia go 5-0 up in the seven-match series as they stayed on course to whitewash their oldest foes.
Set a seemingly challenging 300, master batsman Ponting's 126 - his best ODI score against England, surpassing the 119 he made at Melbourne in 2002 - took Australia to within sight of victory.
They still needed 39 off 36 balls after Stuart Broad had struck twice in the 44th over, Callum Ferguson plumb lbw and Ponting driving to Owais Shah at long-off.
But Cameron White and Mitchell Johnson, who ended the match with a six off Ryan Sidebottom saw them home with 10 balls to spare.
England's batting had repeatedly failed this series.
But here they made 299 - and still it wasn't enough.
Former Ireland batsman Eoin Morgan top-scored with 58 - his best for his adopted country.
But Ponting, who shared a third-wicket stand of 133 with vice-captain Michael Clarke (52), showed how hundreds, not fifties, win games.
Ponting was soon into his stride and struck a huge straight six off left-arm quick Sidebottom.
But on 40 he was dropped by opposing captain Andrew Strauss, a drive off leg-spinner Adil Rashid skimming the England skipper's fingers at short extra-cover on its way to the boundary.
Ponting went on to complete a fifty off 51 balls under the floodlights and two magnificent sixes in as many deliveries from Rashid took him to 97.
A single off Rashid saw Ponting to his 27th hundred in 317 ODIS off 92 balls with three sixes and 10 fours.
Despite losing Clarke and Michael Hussey in quick succession, Australia started the last 10 overs needing 70 more runs for victory.
Earlier 22-year-old left-hander Morgan, a Middlesex colleague of Strauss, reached fifty with a six off Nathan Bracken.
And he later audaciously reverse-hit Bracken for four, a shot Morgan has said previously was developed out of the Gaelic sport of hurling.
But, trying for a repeat next ball, he was caught at short third man.
Fast bowler Johnson saw his 10 overs cost an expensive 80 runs.
Both the new ball duo of Peter Siddle, recalled in place of Brett Lee despite the rested fast bowler's five-wicket haul in Australia's seven-wicket win at Lord's on Saturday, and Bracken started with a maiden apiece.
But Strauss, who after leading England to Ashes glory has won five straight ODI tosses but not much else, was again in good form with three boundaries in four balls off Siddle.
However Strauss, who the previous ball had driven off-spinner Nathan Hauritz back over his head, was given out lbw for 35 by Pakistani umpire Asad Rauf after attempting a reverse sweep having made 63 in both the previous two ODIs.
The under-rated Hauritz led Australia's attack with two wickets for 54 runs.
Morgan revived England's innings with the match's first six, casually hoisting Johnson over long leg.
But he should have been out for 38 when he skied all-rounder Shane Watson to Hussey, who dropped the chance after four juggled attempts.
Morgan's display helped England, again resting the experienced duo of all-rounder Paul Collingwood and paceman James Anderson, score 91 off the last 10 overs.
The series continues with another day/nighter at the same on Thursday.
