Smith, who hit 144 in Australia's first-innings 284, was 46 not out off 61 balls on Saturday. Travis Head is 21 not out in a fourth-wicket partnership of 49 so far.
The pair came to Australia's rescue after Stuart Broad took his 450th test wicket when David Warner was caught behind by Jonny Bairstow for 8 on review. Cameron Bancroft tamely sent the ball to Jos Buttler at short leg for an easy catch off Moeen Ali for 27-2.
England broke through again to make it 75-3 when Ben Stokes forced an edge behind by Usman Khawaja (40), with Australia still trailing.
Smith took a single off Ali at the end of the 22nd over to bring the two teams level before helping to build the small lead. To stop that growing Sunday into something to worry England on a deteriorating wicket — anything over 150 could prove uncomfortable — the hosts need to get Smith out.
England knows that won't be easy.
"You hope he (Smith) makes mistakes," England allrounder Chris Woakes said, "it's a tricky one."
Australia pacer James Pattinson did not want to put a number on how many runs Australia need to win, but added: "Anything over 150 I think. We want to bat all day tomorrow and try to grind England into the ground a bit."
Earlier Saturday, Woakes and Broad ushered England to a 90-run first-innings lead with 374 all out following a middle-order collapse on the third day.
Rory Burns added only eight runs to his overnight score before departing for 133, one of four wickets to fall in the morning as the hosts slipped from 282-4 to 300-8.
A 65-run stand between Woakes (37 not out) and Broad for the ninth wicket added to the lead before England was dismissed and an early tea taken.
When Broad was out for 29 from 67 deliveries, succumbing to Pat Cummins' short-ball tactic, Woakes was left with Jimmy Anderson for company.
England's record wicket-taker, moving gingerly after suffering a calf complaint earlier in the test, contributed three before spooning Lyon into the leg-side, ending a labored final wicket stand during which Woakes turned down a number of singles. While Anderson was able to bat, he did not bowl in Australia's second innings on Saturday. Anderson visited the nets during the lunch break to have a bowl, raising expectations he may play some part.
England's morning wobble saw Burns, Ben Stokes, Moeen Ali and Bairstow also dismissed in quick succession. Stokes was the only batsman to show any fluency, reaching 50 before he aimed a cut at Cummins and nicked through to Tim Paine.
After more than seven hours in the middle, Burns was undone by Nathan Lyon's off spin, edging to Paine who held on instinctively.
Moeen went for a five-ball duck, and Bairstow managed only eight before steering Peter Siddle to Warner at slip.