Smith, back in the Baggy Green 16 months after being banned for his role in the sandpaper scandal, followed a brilliant 144 on day one with an equally fine 142 on day four to become just the fifth Australian to hit twin hundreds against England.
Where the first rescued his side from the cliff edge at 122-8, his second knock of the series helped set a monstrous target of 398.
Matthew Wade also left his mark on the home team, chiming in with a fluent 110 before the declaration came at 487-7.
The more realistic task in front of England is to ensure they are able to bat through for a draw, with first-innings centurion Rory Burns and Jason Roy successfully navigating seven overs before stumps.
They and their nine team-mates must collectively see off another 90 overs on day five if they are to reach Lord’s all square, on a pitch offering plenty of turn for Nathan Lyon.
The 30-year-old Smith from Sydney has single-handedly shifted the course of the match in a way that is rarely seen at this level, batting for 10 and a half hours and 426 deliveries in all, reasserting his dominance on an attack who will surely be having nightmares about the prospect of frunning in to him for the next five weeks.
England will rightly bemoan the loss of James Anderson on the opening morning, a right calf injury restricting their record wicket-taker to four overs and effectively leaving them a man down for the remainder.
Since heading for a scan at lunch on Thursday he has only been on the field for a first-innings batting cameo and may well be required for another before events conclude.
In his ongoing absence England needed a big performance from Moeen Ali but his off-spin provided neither the threat nor the constrictive control the team required.
If figures of 2-130 and an economy rate of 4.48 were not bad enough on a turning pitch, Joe Root’s decision to use 26 overs of part-time spin – his own and Joe Denly’s – spoke volumes.
Moeen’s forgettable day began in the very first over, his fifth delivery slipping inadvertently out of the hand and looping high above Smith’s head for a no-ball. He later repeated the error but it was Moeen’s inability to build pressure that most undermined the team’s plan.
Australia grabbed control in the first session, scoring 107 for the loss of just one wicket to thoroughly dampen the home side’s spirits.
Former Yorkshire player Travis Head was the man to go, Ben Stokes finding the edge, but not before making a spirited 51 and aiding Smith in a vital 130-run stand.
Smith began the day on 46 and added another 52 before lunch, with one mis-hit off Stuart Broad and a flick past a diving leg gully the only moments where he seemed anything less than 100 per cent in control.
Aside from that he moved around the crease and worked nearly every ball where and how he intended.
After taking lunch on 98 he saved one of his best-looking strokes to reach his ton, bisecting mid-off and extra-cover with a sweet drive off Broad.
Smith’s celebration was fittingly composed, the inevitability of the moment clearly not lost on the man at its centre.
Root frittered away a review attempting to get Smith lbw on 125 and a run out chance went begging on 133.
In the end it took the combination of the new ball and Chris Woakes – who did not bowl a single over in the morning session – to land the blow.
Immediately after an elaborate wide Woakes tightened up and found just enough swing to take the edge as Smith aimed through cover.
England’s problem now was that Wade had warmed up nicely against a jaded attack. He scored 71 in a productive afternoon session with a succession of boundaries, allowing no respite when Smith was off strike.
The Tasmania captain, playing his first Test as a specialist batsman after 22 as a keeper, had crept up on them. There was no missing him when he hit his 15th four, a reverse sweep off Root that took him to his first century since January 2013.
He fell to the tireless Stokes before Moeen belatedly made the most of the pitch, ripping one into Tim Paine’s stumps.
James Pattinson (47no) clubbed four sixes as he and Pat Cummins smashed another 78 before the declaration came, England looking thoroughly miffed as their stand progressed.
Burns and Roy were handed a tricky half-hour at the crease, with Lyon, Peter Siddle and Pattinson all taking turns at them. The ball spun wickedly a couple of times but the openers held up their part of the bargain, reaching 13 without loss by stumps.