The brilliant right-hander appeared to toy with the English bowlers at times as he notched his second century of the series.
It was his 22nd Test century and he also passed 1000 runs for the calendar year during the innings.
At lunch the home side was 314 for four in their first innings, with Smith on 139 and Mitchell Marsh on 39, trailing England by 89 runs with six wickets in hand.
Smith resumed on 92 and wasted little time cruising to his hundred, notching the milestone by effortlessly working Jimmy Anderson off his pads for a boundary.
It came from just 138 balls, the fastest century of his career in terms of balls faced, and in his 107th Test knock.
Only Don Bradman (58 innings) and Sunil Gavaskar (101 innings) have reached 22 Test centuries in fewer innings.
England seemed powerless to stop Smith scoring and at lunch he had faced 192 balls, hitting 19 fours and one six.
Smith went to duck under a short ball, but it didn't rise as sharply as he expected and caught him flush on the shoulder.
He also survived an ambitious lbw review from the bowling of Jimmy Anderson on 135, when Chris Gaffaney gave him not out and replays confirmed the ball was clearly missing the leg stump.
The only man out for Australia on the third day was Shaun Marsh (28), who got a thin outside edge to spinner Moeen Ali (1-40) and was caught at slip by Joe Root.
He started nervously and had to contend with the second new ball, but played some crisp shots just before lunch.
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