After Australia resumed on 326-6, the tourists claimed the last four wickets in the day's opening session to dismiss the home side for 385.
That left England with a testing period at the crease before lunch, but openers Alastair Cook and Michael Carberry were able to successfully negotiate the six overs before the break.
England were 24 for none at lunch, with captain Cook looking to emerge from his form slump and on 17, with Carberry on six.
Cook attempted to flick a ball off his pads on three, but instead got an outside edge and it flew to the left of Smith at third slip.
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Smith, who top scored for Australia with a superb 111, dived to his left and got a hand to the ball but couldn't hang on.
With Australia able to regain the Ashes with a win in the third Test, Smith's second Test century, and first on home soil, was the backbone of the home team's first innings.
He had been at the crease for 295 minutes, faced 208 balls and hit 14 fours and two sixes.
The day started well for England, with Stuart Broad (3-100) claiming the wicket of Mitchell Johnson, who had not added to his overnight score of 39, with the second ball of the day.