When bad light stopped play eight overs before scheduled stumps, Amla was on 90 with Kallis providing solid support on 84. Kallis previously held his country's aggregate record with current coach Gary Kirsten at 3592 runs in partnerships throughout 64 Tests and now has surpassed that with Amla following their 136-run unbroken partnership.
At day's end, the pair had accumulated 3607 runs together in their 58th Test. Amla, the number one-ranked Test batsman, passed 5,000 Test runs.
South Africa reached their position of strength through their resolute batting on a flattening wicket mixed with some missed Australian chances and the rub of the green.
The South Africans are bidding to follow up their first-ever series win in Australia on their last tour, in 2008-09.
Kallis had a reprieve on 42 when he miscued Peter Siddle to mid-off where he was held by Nathan Lyon, but umpire Asaf Raud checked back whether Siddle had over-stepped and it was ruled a no-ball.
Injured Duminy out JP Duminy took some gloss off South Africa's brilliant opening day in the first Test by being ruled out of the tour with an Achilles injury following play at the Gabba.
The lower-order batsman was warming down by kicking a rugby ball around with teammates on the playing field, after the Proteas reached stumps at 255 for two, when he suffered the injury.