Amla was 89 not out and De Villiers 70 not out and South Africa 229-3 in its second innings - a lead of 199 - when bad light and then rain ended play an hour early.
With seven wickets in hand and two days to go, South Africa will target a lead of 300-plus, forcing Australia to make a record run chase at Wanderers to win the match and save the series.
The highest successful fourth-innings run chase at the Johannesburg stadium is 294 by Australia six years ago.
South Africa is 1-0 ahead in the two-test series and edging toward its first series win over the Aussies at home since 1970, and first since its was allowed back into international cricket 20 years ago.
Amla and De Villiers eased the pressure on the Proteas after teenage fast bowler Pat Cummins, who took 2-46, struck twice for Australia in the morning to have the home team wobbling at 90-3.
The 18-year-old debutante repaid the faith shown in him in a crucial match when he dismissed opener Jacques Rudolph for 24 and produced a fierce swinging delivery to get rid of dangerman Jacques Kallis (2) just before lunch.
In between, off spinner Nathan Lyon (1-41) forced South Africa captain Graeme Smith (36) to cut straight to Phillip Hughes as the tourists made early inroads and held the initial advantage.
But Australia couldn't break through again on the third day as Amla and De Villiers stayed together through two sessions to take control of the match and the short series for South Africa.
Amla hit 13 fours in his 196-ball innings, while De Villiers collected 10 boundaries and a six off the 122 balls he faced.
The pair both had to grit it out in the early stages of their stand, surviving close lbw calls under pressure from Cummins as well as Mitchell Johnson and Peter Siddle - who both finished wicketless after fading in the afternoon.
De Villiers also shrugged off a painful blow on the toe from a quick delivery from the impressive Cummins.
Cummins struck in the eighth over of the day to boost Australia when Rudolph tried to force a hook shot off a quick, short delivery and sent a catch high into the air for wicketkeeper Brad Haddin.
Smith want to a loose cut shot straight to Hughes at backward point.
Kallis didn't even have a chance to settle.
Australia's second youngest test debutant ever, right-arm paceman Cummins took the crucial wicket of South Africa's top batsman two overs before lunch when his fast out swinger beat Kallis and an edge flew to captain Michael Clarke in the slips.
South Africa was 90-3 and just 60 runs ahead and Australia glimpsed a way back into the series.
But Amla and De Villiers' century partnership in the afternoon moved South Africa toward a significant - and possibly series-clinching - lead as they played cautiously first and then opportunistically later in the day.
They added 97 between lunch and tea and pushed South Africa's lead to the brink of 200 in the 12 overs possible in the final session before light took the players off.
Desperate for a breakthrough, and with Johnson and Siddle struggling to back up Cummins, Australia even turned to Ricky Ponting to bowl late in the day. The 36-year-old batsman's last of his five test wickets was six years ago.
He returned 0-8 off his one over.
