Markram scored 102 not out as he propelled the hosts to 338-6 after they had been put in to bat, to which Australia replied with 227, bowled out with 15 overs to spare.
Keshav Maharaj and Tabraiz Shamsi both took two wickets as their spin halted a brisk Australia response.
However, South Africa did get lucky when David Warner was run out and Tim David was then given out after a review of a catch that looked to have been dropped but was ruled fair by the fourth umpire after a TV review.
Markram also had a touch of fortune about reaching his second ODI century, dropped in the deep on 95 which allowed him to reach the three-figure milestone.
But it was a vital innings that propelled South Africa to a formidable total after they lost their way mid-innings.
They began in rampant fashion as Quinton de Kock and captain Temba Bavuma put on an opening stand of 146 before De Kock was undone by the off-spin of Travis Head and holed out for 82 runs.
Bavuma went quickly thereafter for 57 and the home team’s run rate slowed markedly as Australia pinned them back.
When David Miler departed cheaply in the 42nd over they were 244-5 but Markram revived the innings and ensured a formidable target with some powerful hitting in the last overs.
It did not seem to trouble the tourists, however, with Warner and Head hitting the ball to all corners and Australia racing to 104-1 off 10 overs as they began their reply on a frigid night.
But when Warner slipped, lost his shoe and was run out by Maharaj’s dead-eye throw, despite a despairing dive, the match turned.
Marnus Labuschagne, man of the match in the previous two ODI's which Australia won, was stumped off Shamsi’s bowling for 15 and David adjudged out despite substitute fielder Bjorn Fortuin looking unsure he had taken a clean catch of George Coetzee’s bowling. Television replays were also unconvincing.
Seamer Coetzee then cleaned up the tail to finish with figures of 4-50.
The teams move to Pretoria for Friday's clash with the last game of the series at the Wanderers in Johannesburg on Sunday.
