In his event debut, the 28-year-old drained five consecutive birdies as he tore through the back nine of the Old Course, carding an eight-under 64 to pip playing partner Cameron Young by a stroke at 20-under par.
After starting the day four shots ahead of Smith, Rory McIlroy finished two strokes behind in third after signing off a bogey-free 70.
It meant heartbreak for the Northern Irishman who, looking to end an eight-year major drought, saw a second Claret Jug win slip through his fingers after a day of missed putting opportunities.
Having shared the lead with Viktor Hovland at the summit after a pulsating Saturday duel, McIlroy looked on track to finally clinch his fifth major after pulling ahead of the Norwegian at the fifth hole.
Yet while the 33-year-old subsequently birdied just once more, up ahead Smith — having already doubled the tally by his fifth hole — burst through the back nine with a run of five birdies before adding one more at the 18th.
With Young draining a dramatic final eagle just moments earlier, the Australian’s eighth and final birdie of the round spared him a playoff, his victory assured after McIlroy failed to make the speculative eagle chip needed to draw level.
It sealed a remarkable final day fightback for Smith, whose disappointing 73-shot round Saturday had spoiled an opening 67 and a scintillating 64 that had seen him hold the lead heading into the weekend.
His four-stroke overhaul matched the largest comeback win at St. Andrews, most recently achieved by John Daly in 1995. The triumph also saw Smith become the first Australian to lift the Claret Jug in almost 30 years, after Greg Norman won at Royal St George’s in 1993.
