Man of the match Du Plessis, playing in place of the injured JP Duminy, was 110 not out at the stumps - from 376 balls in over seven and a half hours at the crease.
Resuming on 77 for four with a 430 victory target, the Proteas made it clear their ambitions were limited to a draw as Du Plessis and AB de Villiers scored just 49 runs for the loss of no wickets before lunch.
And when De Villiers (33) was out from the 220th ball he faced, Du Plessis linked up with Jacques Kallis (46) to prolong the frustration for Australia.
Kallis, Dale Steyn (nought) and Rory Kleinveldt (three) perished in the evening session, but Du Plessis and Morne Morkel (eight not out) held firm for the tourists, finishing on 248 for eight as the hosts ran out of time.
The morning was not without alarm for South Africa, with two successful lbw appeals against Du Plessis off the part-time spin of Michael Clarke overturned via DRS.
The first was not out having pitched outside leg stump, while the second was shown on replay to have come off the face of Du Plessis' bat without touching the pad.
Umpire Billy Bowden got both of those wrong, but he had a better moment just before lunch as Australia queried a not-out decision via DRS.
On this occasion, with Du Plessis not offering a stroke, the delivery from Nathan Lyon was shown to be going over the top.
By that time Australia had taken the new ball, and it came into play after lunch as Peter Siddle bowled De Villiers with on off-cutter that went through the batsman's defences, ending the partnership at 89.
Kallis, with the hamstring injury he sustained while bowling seemingly troubling him less than it did in the first innings, struck a four and was dropped early on, before settling into the attritional pattern.
The harder ball inevitably yielded more boundaries with Du Plessis in particular looking good, driving back-to-back boundaries off Siddle.
By tea, he and Kallis had added 78 for the sixth wicket, though there was one more scare in the last over before the break as Du Plessis was dropped by Matthew Wade, standing up to Ben Hilfenhaus.
Du Plessis survived a couple of hairy moments off the bowling of Siddle at the start of the evening session, losing his balance when faced with a yorker and then edging just short of Ricky Ponting at second slip later in the same over, but held his nerve and was soon rewarded with his maiden century.
It arrived with a cover-drive off Hilfenhaus and made him only the fourth South African to post three figures on his Test debut.
The celebrations were cut short, though, as Kallis departed in the next over, edging a Lyon delivery to Ed Cowan at short leg.
Cowan put down another difficult chance offered by Steyn soon after, off the bowling of Siddle, but the paceman snared his man in his next over, caught by a good low catch by Rob Quiney at midwicket.
Kleinveldt hung around for six overs before becoming Siddle's fourth victim, an inswinging yorker seeing off the number nine batsman and leaving South Africa eight down and facing a nervy final four overs.
But Du Plessis and Morkel stood their ground and clinched a hard-earned draw for the Proteas, ensuring the teams will head to Perth all square for the third Test on Friday.
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