Having set the tourists a vast target of 399 in order to win outright on these shores for the first time since 2001, England had Australia in big trouble at 167 for five at tea on day four.
Smith represented an all-too familiar obstacle, having scored 1,251 in his 10 previous innings against England with a lowest total of 76, but was undone for just 23 after flicking Stuart Broad to Ben Stokes at leg-slip.
That was one of three wickets for Broad, who continued his fine series, while there were one apiece for spinners Jack Leach and Joe Root. Matthew Wade was carrying the fight for Australia on 60 not out.
England resumed on 313 for eight overnight, already 382 ahead, and were swept aside in just 18 minutes. Jofra Archer gloved Pat Cummins behind, with an initial not-out verdict allowing Australia skipper Tim Paine to make his first successful bowling review of the entire series.
Broad then took the chance to whip up some early enthusiasm from the crowd, clattering Cummins for a pair of sixes into the leg-side. That brought the psychological barrier of a 400 chase into sight but they fell one short when Leach slog-swept Nathan Lyon to mid-on.
The stage was set for the final act of a compelling series, with Australia’s careworn opening pair first on the field. The tourists’ best first-wicket stand of the summer stood at just 13 and, although they bettered that low watermark by five, it was an unconvincing and brief stay for both men.
Marcus Harris was sent on his way in picturesque fashion, pushing down the wrong line as Broad angled one in and sent off stump cartwheeling. David Warner remains the bigger scalp, though, marked out by his personality and previous pedigree.
Broad removed him for the seventh time in the series by recycling a favourite routine: round the wicket, outside off stump, careless edge, caught at slip.
New Zealand’s John D’Arcy held the previous worst return for an opener across 10 innings of a series, scoring 136 against England in 1958, but Warner’s persistently paltry efforts have brought him just 95.
That brought Smith to the crease, charged with producing another epic alongside his protege Labuschagne. Each got off the mark with drives for four but Labuschagne failed to reach lunch, stretching to cover Leach’s spin only to be beaten on the outside edge. Spotting the back leg just off the ground, Jonny Bairstow completed a sharp stumping.
Smith held the fate of the game in his hands but for once he could not summon something special. Broad was into his third over of the afternoon when he dug one in short towards Smith’s rib-cage, persuading the 30-year-old to flick casually into leg-side.
Unusually, his calculations were off: the shot was too fine and Stokes was waiting at leg-slip, diving to capture the key wicket.
Smith was as surprised as England but walked off to his most generous applause yet having brought his series tally to 774 runs as 110.57.
Mitch Marsh was called back after getting out to a Chris Woakes no-ball on six then saw Rory Burns drop a tough one-handed chance on 13. In the end it took Root’s part-time spin to get him, via a short-leg catch from Jos Buttler.