The Australians, sent into bat after Alastair Cook's first toss win of the series, stormed back from a parlous 97 for five to leave the beleaguered tourists in familiar trouble by opening day stumps.
Australia were all out for 326 late in the day with England losing the wicket of Michael Carberry for a duck to reach stumps at eight for one with Cook on seven and nightwatchman Jimmy Anderson one.
Paceman Ben Stokes finished with six wickets for 99 as easily the best English bowler.
Smith didn't dwell long in the 'nervous nineties' with a six and four off debutant leg-spinner Scott Borthwick to raise his third Test century against England and first at his home Sydney Cricket Ground.
Smith on 99 was gifted with a Borthwick full-toss and he clouted it through to the mid-wicket boundary.
The number five cracked 17 fours and a six in his 154-ball century.
Haddin has had a golden series scoring 465 runs at 66.42 and has played a crucial role in rescuing Australia on a number of occasions in the one-sided Ashes.
Stokes spearheaded the under-manned English bowling attack, which was weakened when debutant Boyd Rankin went off with a hamstring injury while bowling his ninth over.
Stokes claimed the wickets of Ryan Harris, Peter Siddle and Smith in his 20th over to wrap up the Australian resistance.
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