Jansen scored 47 runs off 23 balls as South Africa overcame a slow start to set a formidable target of 315-9 after being sent in to bat first.
He then took a career-best ODI haul of 5-39 off eight overs, as Australia were dismissed for 193 in 34.1 overs.
The win ensured a 3-2 series victory for South Africa, who lost the opening two matches but bounced back with three successive wins to boost morale before next month’s World Cup in India.
The new ball seamed around early in the thin Highveld air and saw South Africa struggle with opener Quinton de Kock, who has announced his retirement from ODIs after the World Cup, out cheaply in his last home innings.
Heinrich Klaassen, who scored 174 on Friday, was then bowled out for six by Adam Zampa, who he had hit to all corners two days earlier.
But South Africa set about the bowling as Aiden Markram and David Miller put on 109 runs in 107 balls for the fifth wicket before the partnership was broken by the first delivery in ODI cricket by part-timer Tim David.
Markram top edged him to Michael Neser, who had dropped him earlier on 81, at deep square leg to depart seven runs short of his century.
David Miller and Jansen then continued the assault with Miller scoring 63 runs. There was also a late cameo from Andile Phehlukwayo, who hits three sixes in the last over to see South Africa past the 300 mark.
Australia did not hold back as they began their response, keeping up the positive approach that has been a hallmark throughout the series, but Jansen took two wickets in the fourth over, dismissing David Warner and Josh Inglis to apply the brakes.
Captain Mitchell Marsh and Marnus Labuschagne put on 90 for the third wicket as Australia stayed well ahead of the required run rate but a potential match-winning partnership ended when Marsh was caught on the third man boundary off Jansen for 71.
The giant bowler then dismissed Labuschagne (44) and Alex Carey (2) with spinner Keshav Maharaj ending any resistance with three wickets of his own at the end.
"These type of performances give you confidence," said Jansen afterwards. "I'd like to play like this more often, which is not easy."
