South Africa captain Graeme Smith made his 18th Test hundred to give his side an outside chance of victory against Australia in Perth.
The tourists were 227-3 at the end of the fourth day's play, after being set a massive victory target of 414.
Smith hit 13 fours in his 108, his first Test century against Australia, before falling lbw to Mitchell Johnson.
Australia were all out for 319 earlier in the day, with Brad Haddin stumped for 94 off spinner Paul Harris (3-85).
The home side were again grateful for the batting efforts of their tail as Jason Krejza and Johnson helped Haddin add 91 vital runs to their overnight 228-7.
It left South Africa facing the daunting prospect of having to make what would be the second highest fourth innings total in Test history to win the game.
Their best so far was making 340-5 to beat Australia in Durban in March 2002.
Should they lose, they will regret their inability to knock over Australia's lower order quickly, with Krejza helping Haddin add 79 for the eighth wicket before he was caught by a diving AB de Villiers at point off Jacques Kallis for 32.
Haddin's fifth half century arrived off 85 balls and he found another useful ally in Johnson, who made 21 but was then caught at first slip by Kallis off Morne Morkel.
It was then a question of whether Haddin could reach a second Test century, having made 169 against New Zealand last month, with only last man Peter Siddle for company.
He struck spinner Harris for two sixes and a four off successive deliveries, but went down the pitch to attempt another big hit off the final ball of the same over and was easily stumped by keeper Mark Boucher.
606: DEBATE
It did not take the left-arm paceman long to make an impact as Neil McKenzie failed for the second time in the game when he edged to the keeper and departed for 10.
Smith met the situation with some aggressive strokeplay and brought up a magnificent hundred with two successive square cuts for four off Johnson.
But the tourists suffered a double blow when Smith and Hashim Amla were dismissed in the space of four overs after a second-wicket partnership of 163.
Smith was deceived by a slower ball from Johnson and Amla, perhaps shaken up by a bouncer the previous ball, failed to move his feet to a full-length delivery from Brett Lee and was caught behind for 53.
"Any century you score is very satisfying personally but there was a bigger picture for me. I really wanted to be there at the end of the day.
"That was one of my big targets but it wasn't to be. It was nevertheless nice to give the scoring some momentum and get the team going," said Smith.
The double setback left Kallis and AB de Villiers to try and rebuild the innings and they did so with some comfort, adding 48 in 11 overs before the close.
Kallis hooked Siddle for six and struck two consecutive boundaries in the next over from Krejza in an unbeaten 33 but he will need to go on to a big score on the final day if South Africa are to go close to reaching their target.
"414 would be an incredible achievement," said Smith.
"We won't arrive tomorrow thinking in terms of 187 [to win]. We need to bat for 55 to 60 overs and the rest will take care of itself."
The world's three leading news agencies are not covering the series due to a dispute with Cricket Australia.
Reuters, Agence France-Presse and Associated Press have suspended all coverage of the 2008-09 season.
Their photographers and reporters did not supply material from within the ground. As a result, we cannot use pictures from the current match.
~RS~q~RS~~RS~z~RS~37~RS~)