The skipper cashed in after being dropped on 35 to reach 142 as the Australians moved within 40 runs of the 352-run follow-on target in reply to England's imposing first innings of 551 for six declared.
At the close on Sunday, Australia were 312 for five with Michael Clarke on 30 and Adam Gilchrist on 13.
It was 31-year-old Ponting's 10th century in his last 13 Tests -- he has played in 107 in all -- and took him past previous captain Steve Waugh's 32 centuries off 168 Tests.
Scorecard of 2nd Test Day 3
Ponting now ranks outright fourth all-time behind Sachin Tendulkar (35), Brian Lara and Sunil Gavaskar (both 34) as the scorer of most hundreds in Tests.
Hussey, bowled for 86 in Brisbane, had the anguish of missing out on another deserved century when he played on and was bowled by seamer Matthew Hoggard for 91 in almost five hours with 30 minutes left to stumps.
The West Australian left-hander, who survived a line-ball run-out decision on 70, lifted his impressive batting average to 77.41 in his 13th Test.
Ashley Giles felt the pain of Ponting's century more acutely than others in the England team after dropping him on 35 off Hoggard with the Aussies at 78 for three.
Giles, positioned square just inside the boundary ropes, leapt high for the two-handed chance but could not hold the catch in a major let-off. Ponting went on to score 107 more runs.
Ponting and Hussey restored the Australian innings with a 192-run partnership after the loss of two wickets had them a nervous 65 for three.
It was 22 runs short of Australia's record fourth partnership at the Adelaide ground, set in 1988-89 by Dean Jones and Allan Border.
Ponting, who has been the bane of the England bowlers in the series with scores of 196 and 60 not out in the first Brisbane Test, was finally out caught behind in Hoggard's first over of the second new ball.
That swelled his series tally to 398 runs at an average of 199 and lifted his career Test average of 60.06 in his 107th Test match.
Only Hussey has a greater Test average among contemporary Test cricketers.
Ponting, who batted for 353 minutes and faced 245 balls with 12 boundaries, was also close to being run out on 46 when Paul Collingwood's direct throw just missed the stumps at the bowler's end with the Aussie skipper well out of his ground.
Hoggard also claimed the wickets of Matthew Hayden (12) and Damien Martyn (11) and following Saturday's wicket of Justin Langer (4) to finish the day with 4-76 off 27 overs.
Hayden, who struggled in last year's series with 318 runs, inflated by his 138 in the fifth Test, followed an outswinger and edged to wicketkeeper Geraint Jones leaving Australia 35 for two.
Martyn, whose Test place is under growing pressure following his 29 in Brisbane and a poor Ashes series last year, followed in the 23rd over when he was snapped up low down by Ian Bell in the gully.