Australia, well-placed at 97 for one, slumped to 106 for five as four wickets fell for just nine runs in 36 balls.
At tea, the Ashes-holders were 162 for seven, with their hopes of scoring the further 250 runs they need to reach a record-breaking target of 412 all but scuppered.
Fast-medium bowler Broad had tea figures of three for 22 in 10 overs, with Australia's hopes of salvaging a draw currently resting with Mitchell Johnson (26 not out) and Mitchell Starc (four not out) following the dismissal of all their specialist batsmen.
But Ashes-holders Australia were going along well at 97 for one following the early exit of Chris Rogers when they lost his fellow left-handed opener David Warner lbw for a well-made 52 to off-spinner Moeen Ali on the stroke of lunch.
Broad had bowled superbly in an opening spell of one for 10 in six overs and probably deserved more than the wicket of Rogers.
Broad was on target in the first full over after lunch when he seamed the ball away from Smith, the world's number one ranked Test batsman, who could only open the face and edge a comfortable catch to Ian Bell at second slip as, for the second time this Test, he fell for 33.
Clarke, one of the outstanding batsmen of his generation and looking to lead Australia to their first Ashes series win in Britain in 14 years, having featured in all three subsequent losing tours, then went for just four when, reaching for a drive, he guided Broad to Ben Stokes at backward point.
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