South Africa's stand-in captain Eben Etzebeth lauded the 23-year-old in the build-up to Sunday's (AEST) encounter, and the scrum-half put in an inspired display at Ellis Park.
Having opened the scoring in the 11th minute, Jantjies played a crucial role in South Africa's second try from Lood De Jager before capping his stirring display with another five-pointer just after the hour.
Dane Haylett-Petty got on the board for Australia, although he missed a golden chance to put the Wallabies in front heading into the break.
The Springboks made their good fortune count, Taniela Tupou's yellow card proving costly for Australia as S'busiso Nkosi and Jantjies ran in while the Wallabies were down to 14, with Cobus Reinach's late try ensuring a bonus point.
With the tournament shortened to three rounds because of the upcoming Rugby World Cup, Australia's chances of success already look slim, and the pressure seems to be mounting on coach Michael Cheika.
Australia looked in good shape when it forced an early lineout deep in South Africa's half, but found itself behind a minute later when Jantjies rounded off a wonderful counter after fine wing play from Nkosi.
Lukhan Salakaia-Loto saw a try disallowed as Australia rallied, with the Wallabies handed a boost when Andre Esterhuizen was sent to the sin bin after 20 minutes.
Despite its numerical disadvantage, it was South Africa that struck next, De Jager forcing the ball down after Jantjies had been hauled down a metre out.
Haylett-Petty exploited a gap in South Africa's line to reduce the deficit to four points before the half-hour mark, but the Wallabies winger was later left red-faced when he fumbled what looked to be a simple pick-up on the Springboks line.
Australia failed to pick up where it left off after the break and was fortunate when Elton Jantjies, whose kicking had been on point in the first half, failed to convert a penalty.
Tupou's dangerous lunge during a ruck reduced Australia to 14 men soon after, and South Africa wasted little time in capitalising when Nkosi dived over in the corner before Jantjies helped himself to a second try.
Jantjies was taken off to a standing ovation soon after, and although Bernard Foley's try and subsequent conversion threatened to make things interesting, Reinach added further gloss to a convincing triumph after the hooter had blown.