Together with Michael Clarke, Ponting shared a third-wicket stand of 112 as Australia reached their target of 248 with 16 balls to spare.
Clarke was 55 not out off 63 balls and Andrew Symonds, who finished the match with a four off Sajid Mahmood, unbeaten on a run-a-ball 28.
Although England didn't require a victory to keep their semi-final hopes alive, this defeat left them needing to win all three of their remaining Super Eights matches against Bangladesh, South Africa and the West Indies while hoping other results go their way.
Victory meant Australia, chasing an unprecedented third straight title, had gone 24 unbeaten at the World Cup since a 10-run defeat against Pakistan at Headingley in 1999.
Kevin Pietersen's maiden World Cup hundred was the cornerstone of England's 247 all out.
Pietersen, whose 104 was England's first century this World Cup, put on 140 for the third wicket with Ian Bell (77) after his side slumped to 24 for two.
But Australia fought back by taking three wickets for 15 runs in six overs as England declined from 164 for two to 179 for five.
Openers Adam Gilchrist (27) and Matthew Hayden (41) saw Australia off to a brisk start before the former was caught by Paul Collingwood at square gully off Andrew Flintoff.
Hayden was clean bowled by Durham medium-pacer Collingwood after playing down the wrong line.
Runs were then hard to come by and Ponting, on 21 had given up when opposing captain Michael Vaughan's throw from mid-wicket just missed the stumps with the batsman yards out.
Ponting appeared to be easing his his way to a 24th one-day international hundred when he was run out, sent back by Clarke for 86, by Collingwood's direct hit running round from point. He faced 106 balls with 11 fours.
Pietersen nearly caught Symonds on four, but the umpires correctly ruled he didn't have full control as he threw the ball back in over the boundary before crossing the rope.
Earlier, left-arm quick Nathan Bracken had an economical three for 33, fast bowler Shaun Tait three for 41 and Glenn McGrath, in what could be his last match against England before retirement, three for 62.
Just 51 runs came in the last 10 overs with Pietersen, whose fourth century at this level came off 117 balls with one six and six fours, scoring one boundary between fifty and a hundred.
England saw skipper Michael Vaughan (five) and Andrew Strauss, normally an opener but batting at three after Middlesex team-mate Ed Joyce was dropped, both played on to Tait.
Vaughan's early exit after winning the toss meant he'd now scored just 83 runs from six tournament innings.
Pietersen, who had his tour of Australia ended when McGrath broke his rib in Melbourne in January, was dropped twice.
On 50 Ponting failed to hold a tough one-handed chance at mid-on and, with Pietersen on 63, Hayden somehow floored a seemingly simple two-handed catch at mid-off.
Australia, beaten 2-0 at home in England in the CB series finals before a five-wicket warm-up win in St Vincent last month, then regained control.
Bell drove McGrath straight to Michael Hussey at cover to end a 90-ball innings with nine fours and Collingwood (two) was caught behind off Tait.
Flintoff's wretched time with the bat continued when he misread left-arm wrist spinner Brad Hogg and was stumped by Gilchrist for four.
England, as happened in Wednesday's agonising two-run defeat against Sri Lanka, had seen a promising position disappear.
Pietersen fell in the penultimate over when he holed out against Bracken to Clarke at long-off.
England play Bangladesh, shock conquerors of South Africa on Saturday, in Barbados on Wednesday with Australia in action there two days later against Ireland.