That left Australia, 2-0 down in the five-match series after a drawn third Test meant they couldn't regain the Ashes, 163 runs behind England's seemingly modest first innings 238.
Chris Rogers was 41 not out and Steven Smith 17 not out, with Broad taking three wickets for 23 runs in seven overs.
England, 238 for nine overnight, failed to add to their total before last man James Anderson was bowled by Jackson Bird.
And 12 for one became 12 for two when Broad, taking two for none in seven balls, had Usman Khawaja, uncertain whether to play or leave, caught behind for a duck off the bottom edge by wicketkeeper Matt Prior.
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Once again Clarke, Australia's best batsman, who made a brilliant 187 -- the tourists' only century of the series so far -- at Old Trafford, came in with his side in trouble.
However, the latest controversy involving the Decision Review System this series was not long in coming when Hill gave Rogers out caught behind off Broad on 20.
This time Rogers reviewed and the much-criticised Hot Spot element of the DRS indicated he hadn't hit the ball.
Although the ball hit Rogers' back pad, Hawk Eye tracking technology said the ball was just clipping the bails and the 'umpire's call' verdict meant Rogers, who subsequently hit several well-struck boundaries, was not out lbw either.