On Sunday, Amla and Quinton de Kock, the 21-year-old batsman on debut, shared a partnership of 64 for the fifth wicket to move South Africa on and set the big total, with the Proteas adding 78 to their overnight 192-4.
Amla was sublime for his century and stroked 16 flowing fours in all, most of them sumptuous cover drives.
De Kock hit three fours but was out for 34 when caught by Michael Clarke at slip for offspinner Nathan Lyon's only wicket of the innings and Australia's lone breakthrough of the day.
JP Duminy was 18 not out with Amla and was clearly intent on moving things on with his two boundaries before the declaration came.
South Africa was 447 runs ahead when captain Graeme Smith called the two batsmen in, giving his team half an hour before lunch to bowl at the Australians.
Rogers was immediately into his stride with drives to the boundary to survive the first mini-test and go to 21 not out. David Warner was 10 not out at the break.
South Africa bowled Australia out for 246 in just 57 overs in the first innings and has five more sessions to bowl at the Australians and push for victory if the weather doesn't intervene.
However, the home team was also hampered by a groin injury to left-arm seamer Wayne Parnell, who won't be able to bowl in the final innings, depleting South Africa's attack.
