At lunch on the second day, Australia were 392 for five with Clarke 168 not out -- his highest Test score against England -- in a match the tourists, 2-0 down with three to play, had to win to have any chance regain the Ashes.
Brad Haddin, dropped on 10, was unbeaten on 18.
England were indebted to off-spinner Graeme Swann, who took two wickets in the session on his way to innings figures of four for 103 in 31 overs, for ensuring Australia did not have things all their own way.
On another sunny day and on a still good pitch, Smith was quickly into his stride with a stylish cover drive for four off James Anderson, still to take a wicket this match on his Lancashire home ground.
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Clarke, on 136, drove uppishly but powerfully off Tim Bresnan only for Swann, very close in at short extra-cover, to parry the fast-travelling chance above his head.
But a stand eventually worth 214 ended when Smith, eyeing a maiden Test hundred, top-edged a slog off Swann's sixth ball Friday and holed out on 89 to Jonny Bairstow at midwicket, leaving Australia 343 for four.