Joe Root's men did themselves no favours when they lost three wickets for four runs, and their last six for 56, after a stand of 83 between Dawid Malan (56) and Moeen Ali en route to an apparently under-par 302 all out.
But they responded in the field by sticking to their captain's effective plans with sustained, accurate spells, until Smith (64 not out) emerged from the home pack to revitalise his team from 76 for four to 165 without further loss at the close in an unbroken stand with Australia's returning number six Shaun Marsh.
Smith needed to be at his most watchful and determined on his way to a hard-earned 112-ball 50 after four England bowlers had taken a deserved wicket each.
Stuart Broad was rewarded first, when debutant opener Cameron Bancroft pushed out on the front foot and was very well caught behind by a diving Jonny Bairstow.
Usman Khawaja was lbw to one that did not turn from Moeen, brought on after just eight overs by Root.
England kept David Warner becalmed throughout, and the combative opener blinked first when he whipped Jake Ball to midwicket, where Malan was relieved to take a sharp catch at the second attempt.
James Anderson then out-thought Peter Handscomb to have him plumb lbw, a dismissal which required a review to overturn the initial decision but should not have done.
That was as good as it got for England, who were undone by Smith.
Marsh too grew in confidence towards the end of a stamina-sapping examination for the touring attack, who nonetheless will still be able to resume with realistic designs on a first-innings lead.
England had managed to add 105 more runs to their overnight total in an extended first session, thanks largely to Malan and Moeen.
While the fifth-wicket pair were prospering, though, Root must have been hoping for substantially more than a mere 300 benchmark.
It was not to be.
Malan became the third of England's Ashes novices to pass 50 here at his first attempt, and there were some authoritative drives among his high boundary count of 11.