The touring side, 3-1 down in the series and bidding for a consolation victory after losing the Ashes, made a solid start after losing the toss with David Warner scoring 85 and Chris Rogers 43.
England, however, removed both openers and captain Michael Clarke for 15 to expose the fragile Australian middle order before Smith batted with calm authority in a partnership with Adam Voges that put their side in control of the match.
Voges will resume on 47 not out and Australia will look to build a large total to put England under pressure in their bid to win four home Ashes Tests in a series for the first time.
Rogers, playing his last Test, and Warner had adopted a risk-free strategy in overcast conditions with memories of their collapse to 60 all out on the first morning of the last Test fresh in their minds.
They scored only 19 runs in the first hour and the first boundary came in the 15th over, the pair trying hard to lay a platform for their team after England regained the Ashes last week in Nottingham.
Australia took lunch on 82 for no wicket and the openers increased the scoring rate after the interval.
They looked in control until Rogers was surprised by a lifting ball from Mark Wood, edging a catch to first slip which Alastair Cook took at the second attempt to end a stand of 110.