Australia were 295 all out off the final ball of the second day, 12 runs ahead, as Smith rode his luck to top-score with 71 following a scare just after tea.
The 21-year-old son of former England all-rounder Mark Ealham looked to have replicated Ricky Ponting’s famous 2005 dismissal by the unknown Gary Pratt, combining with wicketkeeper Jonny Bairstow to leave Smith diving for the line.
Smith initially looked bang to rights but, instead of departing for 44 and leaving his side 195 for eight, he was reprieved by TV umpire Nitin Menon.
Replays suggested Bairstow had begun to nudge one of the bails loose with his arm before collecting the ball cleanly and there was some debate over whether either bail was fully dislodged before Smith’s bat slid home.
What mattered most was the ‘not out’ decision that appeared on the big screen and the 100 runs which followed.
That was easily Australia’s most productive period of a day that had seen them embark on pedestrian go-slow in the morning session and a jittery collapse in the afternoon.
Having watched England blaze 283 in 54.5 overs, Australia crept just above that mark in 103.1, Ben Stokes taking an excellent two-stage boundary catch to end the innings in the closing moments.
England were one bowler down due to Moeen Ali’s groin strain, but Australia came out with nothing but survival on their mind, Usman Khawaja and Marnus Labuschagne scoring just 13 runs off the bat in a first hour that tested English patience in the field and in stands.
Labuschagne was completely bereft of intent, scratching out nine off 82 deliveries before Mark Wood finally drew the outside edge England had spent almost 90 minutes probing for.
It looked a regulation catch for Bairstow but he froze on the spot, leaving Joe Root to hurl himself into action at first slip and claim a brilliant one-handed grab. That was the height of the pre-lunch entertainment, with the scoreboard trudging to 115 for two by the break.
Australia had put miles in the English legs and taken time out of a game their rivals need to win, but they had barely moved the dial in real terms.
The limitations of that approach were exposed in the afternoon, with England taking five for 71 to take control of proceedings. Stuart Broad played the role of ringleader, dismissing Khawaja and Travis Head in successive overs to inject some electricity into a game that had gone to sleep.
Khawaja had spent more than four-and-a-half hours in defiance when Broad speared one in from round the wicket and trapped the left-hander in front of leg. Five balls later the seamer was celebrating again, challenging Head outside off stump and getting the nick.
England continued burrowing through the middle order as James Anderson belatedly opened his account for the match in the 16th over, bowling Mitch Marsh off a hefty inside edge and cracking a long overdue smile in the process.
The mistakes kept coming, Alex Carey chipping Root’s tempter to short cover and Mitchell Starc flapping Wood straight up in the air.
Smith was shaping up to be the key figure as he reached tea on 40, but he came desperately close to a self-inflicted dismissal.
Turning back for a second as Ealham sprinted in from the deep and flung a flat throw to the keeper, he looked to be struggling as he dived for his ground.
Replays initially seemed to seal his fate, with his bat short of the crease line as the stumps were broken. He was halfway to the pavilion when he sensed something might be amiss, with the slow-motion footage suggesting Bairstow had nudged one bail loose before gathering the ball in and parting the stumps.
The images were scrutinised for a couple of minutes, analysing when and where the bails left their grooves, before Menon ruled in Smith’s favour. His decision was met with frustration among the home supporters and a healthy dose of confusion elsewhere, as the assembled pundits tried in vain to bring some clarity.
Smith added another 44 before skying Chris Woakes over his shoulder to Bairstow, who did his work well this time.
England should still have taken a lead into day three but struggled to mop up the tail. Pat Cummins made an assured 36 and Todd Murphy landed three sixes on his way to 34.
Woakes had the skipper lbw late on and Root finished things off when Stokes affected a smart catch-and-release take on the boundary to dismiss Murphy.
England will bat again on day three, with barely an inch to separate the sides.