Having ended the first day on 196-4, England extended their tally through Dawid Malan (56) and Moeen Ali (38) - a profitable partnership of 83 for the fifth wicket - before losing their last six wickets for just 56 runs.
The momentum appeared to be in Australia's favour as they began their reply but they found themselves on the ropes by tea with four wickets down for just 76 runs.
David Warner could only contribute 26 before his short chip found Malan just before tea, Peter Handscomb (14) then falling to James Anderson to leave the Aussies in danger of an embarrassing collapse.
Over to Smith, however, who put in a resolute display at the crease with 64* - his 22nd Test fifty - to steady the ship alongside Shaun Marsh (44*).
Australia will enter the third day trailing England by 137.