South Africa will record their first home Test series win over Australia since the end of apartheid, having successfully batted the tourists out of the contest in Johannesburg.
Australia, set an insurmountable target of 612 at tea on day four of the fourth Test, will resume at 3-88 on day five.
Batting through three sessions on Tuesday would be a moral victory for the visitors, reeling from the cheating scandal that resulted in Steve Smith, David Warner and Cameron Bancroft returning home in shame.
Unbeaten batsmen Shaun Marsh and Peter Handscomb successfully stonewalled their way to a draw in Ranchi last year, while forecast showers could also help Australia's hopes of denying South Africa victory.
But even if the match is drawn - a big if based on the tourists' first-innings collapses of 3-28 and 3-6 - then the hosts will celebrate a 2-1 series triumph with much gusto.
"We have a massive goal ... we've been quite hard on that goal," Proteas opener Dean Elgar said,
"It (declaring with a lead of more than 600) was a first for me and I'm glad I was in the happier dressing room."
The Proteas' most recent home Test series win over Australia came in 1970.
South Africa had failed in seven home series against Australia since being welcomed back to international cricket in 1991.
That history is part of the reason that Faf du Plessis took such a conservative approach, overcoming a painful finger injury to score 120 then finally declaring at 6-344.
"It would have been nice to be one or two down," Australia captain Tim Paine told SuperSport.
"We've got a chance to save a Test.
"We'll turn up tomorrow and fight as hard as we can."
The other factor in du Plessis' caution during an innings that spanned 105 overs was the niggles being nursed by pacemen Morne Morkel (side strain), Kagiso Rabada (sore back) and Vernon Philander (groin). The trio all bowled on Monday, but aren't fully fit.
Morkel trapped jetlagged openers Matthew Renshaw and Joe Burns lbw, for five and 42 respectively, while Usman Khawaja's spin struggles continued when he was judged lbw on seven.
Khawaja reviewed, protesting that he offered a shot to the delivery from Keshav Maharaj that kept low, but controlling umpire Nigel Llong was having none of it.
A pitch invader, who scored a handshake from Dean Elgar, temporarily delayed the Proteas' push for victory after tea but Morkel created the initial breakthrough soon after in his second over.
History suggested the Proteas had enough runs on the board in Monday's morning session. West Indies' 7-418 remains the Test record for a successful run-chase.
"We want Test match cricket to survive and be exciting, this is not a good advertisement for the game. Get on with it & declare," Shane Warne fumed on Twitter.
Du Plessis, averaging 9.17 in the series before his final innings, found form after weathering two painful blows to the gloves.
Pat Cummins dismissed du Plessis and Quinton de Kock on Monday, taking his match haul to a career-best 9-141.