Offspinner Swann was on a hat-trick after getting some turn to have Hussey dismissed seven runs short of his century and next ball had recalled paceman Ryan Harris leg-before-wicket for a duck.
Hussey, dropped in a return catch by Anderson when on three, was on track for his third consecutive Ashes century before he was deceived by a turner from Swann and was snapped up by Paul Collingwood at slip.
The veteran left-hander, who scored 121 in the second innings at The Oval last year, hit 195 in the first Gabba Test last week and was looking in good touch to make it three in a row.
Hussey had helped restore Australia's parlous position with a 51-run stand with Haddin and it was big wicket for England.
Harris was struck on the back pad at the crease but called for a review by the third umpire, who confirmed South African umpire Marais Erasmus's decision.
Xavier Doherty saw off the hat-trick threat, but became the second run out victim of the day in a mix-up with Haddin, who went on to make 56.
Graeme Swann celebrates after picking up Ryan Harris during the second Ashes Test in Adelaide
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