Smith dominated proceedings as his 26th Test hundred – and third double against England – took his series tally to 589 in four innings and his total crease occupation to a shade under 24 hours.
England had chances to get him, Jofra Archer missing a caught and bowled chance on 65 and Jack Leach having him caught at slip only to see the wicket scrubbed off for a front-foot no-ball.
He was last man out, home captain Joe Root his unlikely downfall courtesy of a leg-break reverse swept to short third man, but a late flurry of 59 runs in 49 balls from Nathan Lyon and Mitchell Starc persuaded Tim Paine to call his men in and have a late bowl at England's openers.
England had their chances but Jofra Archer failed to gather a caught-and-bowled when he was on just 65 and when Leach had him caught at slip on 118 he was summoned back to the crease after replays showed the spinner had no-balled.
He put on an unbroken 145 with Paine who was also dropped twice, by Jason Roy and substitute fielder Sam Curran, on his way to 58no.
England will rue the fact they did not get Smith in a nervy period at the start of play, with Stuart Broad beating the batsman with the first two balls of the morning as he resumed on 60.
Archer kept the pressure on at the other end and should have had Smith with his third delivery, a low, full toss which was pushed straight back at the seamer.
It appeared to be a relatively-simple return chance but Archer failed to get a firm hand on it and a golden opportunity for England turned into four runs for Australia.
Smith was being challenged, Archer drawing an inside edge that squirmed into the leg-side and then testing him with a more threatening bouncer than any he had managed on day one, but each minute that he spent in the middle seemed to reduce the bowler's advantage.
An effortless steer to the third man boundary off Broad suggesting he was finding his feet once again and he soon began to accumulate effortlessly.
England were able to put an end to Travis Head's sketchy innings of 19, Broad's round-the-wicket angle to left-handers racking up another victim as he picked up his second lbw of the Test and 17th wicket of the series.
Matthew Wade was next to abandon Smith, making a deeply-unconvincing 16 before racing down the pitch in a bid to smash Leach over the top.
Instead of the mighty connection he envisaged, the ball soared skywards and eventually dropped into Root's hands at mid-on, notwithstanding a few nervy
moments as England waited underneath.
Smith moved to 99 with 10 successive singles and then flicked Craig Overton to mid-wicket for two to bring up his 26th Test century, 11 of which have come against England.
England should have started the afternoon session with the scalp of Paine, who nicked a wide one from Broad on nine only for Roy to fumble the chance.
Remarkably, things only got more frustrating from there. First Smith hoiked Leach wildly into the off-side, but safe between two fielders, on 108 then he banked back-to-back boundaries off Ben Stokes – the second a brilliantly-precise steer to the left of gully.
Then came the killer moment, Leach finding the outside edge and Stokes holding a smart slip catch. England finally had their man and Stokes' reaction – hurling the ball into the ground with force – showed how much it meant.
Then a pause as Smith was told the replays were being checked. Leach had overstepped and England's bubble was burst.
Their best hope now was the new ball but its arrival was a false dawn, Smith digging back in after his reprieve to go past 150 and Paine upping his share of the workload.
Root sent for Stokes to make something happen but he lasted just five balls, wincing in pain before admitting defeat and spending 20 minutes off the field receiving treatment on a sore shoulder.
The blows kept coming for the hosts, Curran dropping Paine on 49 after he mis-hit Archer to mid-on.
Australia piled on 128 in 25 overs after tea, Smith eventually falling to Root's part-timers only for Starc to pick up the baton with 54 in 58 balls.