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, to dismiss Callum Ferguson plumb lbw and have 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 Australia 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.
This was only Ponting's second match back since his post Ashes break and the 34-year-old was glad Australia had maintained their winning streak ahead of the Champions Trophy, which starts next week in South Africa.
‘I felt good all day,’ said Ponting. ‘Michael Clarke and myself got us in a position where I would have been disappointed if we hadn't won the game. It shows our one-day cricket is going the right away ahead of the Champions Trophy.’ He added: ‘Anyone we've rested over the last few years has generally come back and played really well.’
Former Ireland batsman Eoin Morgan top-scored for England 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.
England captain Andrew Strauss said his side's batting had improved but that several misfields had let them down.
‘The batting was bolder and Eoin Morgan embodied that but the fielding was poor, there was no excuse. In a tight game, you don't want to let yourselves down in an elementary area.’
Ponting was soon into his stride and struck a huge straight six off Sidebottom.
But on 40 he was dropped by 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 near run-a-ball fifty 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.
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 developed out of the Gaelic sport of hurling.
But, trying for a repeat next ball, he was caught at short third man.
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.
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 after attempting a reverse sweep having made 63 in both the previous two ODIs.
Morgan should have been out for 38 when he skied all-rounder Shane Watson to Hussey, who dropped the chance after four juggled attempts.
The series continues with another day/nighter here on Thursday.