South Africa were in a strong position thanks to half-centuries by Kallis (54), AB de Villiers (64) and Ashwell Prince (50), but they lost their way after tea as Australia took six wickets for 25 runs in 11 overs.
The home side were all out in 71 overs, having won the toss and chosen to bat at the Wanderers.
Peter Siddle claimed three for 69, while spinners Nathan Lyon and Michael Clarke took two wickets apiece as South Africa let a weakened Australian attack off the hook. The visitors were a man down for most of the day after seamer Shane Watson limped off with a hamstring strain.
Kallis played with tremendous authority and a sumptuous cover drive sent his first ball, bowled by Watson, racing to the boundary and drew him level with West Indian left-hander Brian Lara on 11,953 runs.
He then took a single off his third delivery to surpass Lara, leaving only Sachin Tendulkar (15,086 in 183 Tests),Rahul Dravid (12,979 in 159 Tests) and Ricky Ponting (12,495 in 155 Tests) ahead of him on the run-scorers' list.
Score board
SOUTH AFRICA (I Innings):
Rudolph c Haddin b Watson 30
Smith c Clarke b Johnson 11
Amla c Ponting b Cummins 19
Kallis c Khawaja b Siddle 54
De Villiers c Cummins b Siddle 64
Prince c Johnson b Lyon 50
Boucher c Lyon b Siddle 3
Philander lbw Lyon 0
Steyn (not out) 15
Morkel c Watson b Clarke 6
Tahir c Hughes b Clarke 0
Extras (B-9, LB-2, W-2, NB-1) 14
Total (all out, 71 overs) 266
Fall of wickets: 1-24, 2-43, 3-123, 4-129, 5-241, 6-243, 7-243, 8-245, 9-258.
Bowling: Johnson 16.1-4-67-1, Cummins 15-3-38-1, Siddle 15-4-69-3, Watson 3.5-1-13-1, Lyon 13-2-52-2, Hussey 4-0-10-0, Clarke 4-1-6-2.
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