Anderson accounted for two of the three wickets to fall in the first 10 minutes, made a key dismissal just after lunch and then returned to remove the penultimate Australian batsman to finish with figures of 4-51.
England openers Andrew Strauss and Alastair Cook faced one over from Ryan Harris, which netted one leg bye, to leave England 1-0 at the close of play.
Australia's Mike Hussey, who made 195 in the drawn first Test at the Gabba, again offered the sternest resistance to the tourists but spinner Graeme Swann dismissed him for 93, precipitating the collapse of the tail.
Having lost the toss at a ground which is traditionally batting-friendly and where huge first innings totals are the norm, England were expected to spend a long, hot day toiling in the field with little return.
Anderson clearly had other ideas, however, although the first wicket to fall came courtesy of Australian confusion.
The match was just four deliveries old when Watson set off for a single off his pads but Katich, who had not faced a ball, failed to react and was left fuming as Jonathan Trott fired a direct hit from midwicket.
The next ball removed Ponting for a golden duck, the Australian skipper getting an outside edge to an Anderson delivery and Graeme Swann swooping to catch it at second slip.
Ponting, the most prolific Test batsman of all time at the Adelaide Oval, looked as angry as Katich to have marked his 150th Test with his fifth duck.
Vice captain Clarke, who again looked out of sorts, lasted just seven minutes before Anderson and Swann combined to dismiss him for two runs.
Anderson thought he had added Watson to his list of victims soon afterwards but his loud lbw appeal was ignored and the tv review showed the ball to be going over the stumps.
The impressive English quick also dropped a difficult return catch off Hussey, a let-off, which the Australian mid-order batsman looked to, determined to exploit.
Anderson finally got Watson two overs after lunch when he managed to find some swing which fooled the batsman into a shot which ended up in the hands of Kevin Pietersen at gully.
England kept plugging away as Hussey accumulated runs and Steve Finn accounted for Marcus North caught behind for 26.
That dismissal reunited Hussey with Brad Haddin, however, and for a while it looked like the pair might reprise the partnership of 307 they enjoyed in the first Test.
Swann finally separated them when he finally got some real movement and Hussey plonked the ball to Paul Collingwood at first slip.
Swann added Harris's wicket lbw on the next ball but was unable to complete a hat trick when new batsman Xavier Doherty fended off the first delievery he faced.
Haddin continued to battle on bravely on his own but, running out of partners, he barreled a Stuart Broad to Finn out by the boundary to end the innings with a 56.
