The pair rammed home the advantage with an unbeaten century stand as the world's best team blunted the Australian attack to have the South Africans in command after winning the toss.
When bad light stopped play eight overs before scheduled stumps, South Africa were 255 for two with Amla unbeaten on 90 and 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 partnership for the third wicket.
At day's end, the pair had accumulated 3607 runs together in their 58th Test while 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.
It was a strong statement of intent by the South Africans in their bid to follow up their first-ever series win in Australia on their last tour, in 2008-09.
Kallis had a reprieve on 42 in the over after tea when he miscued Peter Siddle to mid-off where he was safely held by Nathan Lyon, but umpire Asaf Raud checked back whether Siddle had over-stepped.
Replays showed Siddle's heel on the line and the TV umpire ruled a no-ball for Kallis to stay at the crease much to Australia's anguish.
Siddle added to Australia's frustrations when he put down a regulation caught and bowl chance six overs later when Amla was on 74 and South Africa at 206 for two.
Skipper Graeme Smith was out following a review in the 11th over after umpire Billy Bowden initially turned down James Pattinson's lbw appeal.
Television replays clearly showed the ball hitting Smith's back pad in front of the wicket and he was given out, with Pattinson enthusiastically celebrating the verdict.
Alviro Petersen had a controversial let-off when he appeared out lbw to a Ben Hilfenhaus inswinging yorker when on 51.
The Australians went for their third referral but the TV umpire ruled "umpire's call" despite replays showing the ball first hitting Petersen's leading foot and projected by Hawkeye technology to be heading for middle and off-stump.
It left Australia without access to further reviews for the rest of the South African innings.
But Petersen threw away his wicket on 64 when he hit Nathan Lyon straight to Michael Hussey at mid-on in the 39th over.
He angrily swooshed his bat in the air having passed up a good chance of his fifth century after spending 168 minutes at the crease.
Michael Clarke used six bowlers -- even the modest medium pace of debutant Rob Quiney -- in a bid to winkle a breakthrough, but it was a day the Australians were wanting to put behind them as they bid to stay unbeaten at the Gabba ground for 24 years.
Australia earlier left out paceman Mitchell Starc and went with the spin of Lyon while the Proteas gave Rory Kleinveldt his Test debut in a four-strong pace attack.