Jacques Rudolph posted his sixth test century and second against New Zealand to help cement South Africa's dominant position.
The visitors declared at 435 for five - a nice round figure of 400 runs ahead - having resumed at 268 for three.
In reply, New Zealand was 137 for two at stumps and need a further 264 runs to seal an unlikely win.
New Zealand's biggest successful run chase in the fourth innings was 324 for five against Pakistan in Christchurch in February 1994.
There is hope, though, in the way Brendon McCullum and Ross Taylor are bating. The pair looked in majestic form. McCullum raced to 50 from 65 deliveries, and Taylor belted some fabulous cut shots. Both will resume today with McCullum on 58 and Taylor on 48.
The visitors resumed with Rudolph on 13 and Jacques Kallis looking to add to his total of 107.
Kallis combined with Graeme Smith for a third-wicket stand of 200 runs on day three to put the visitors in a commanding position but could not build on his impressive innings, holing out to mid-wicket for 113.
Rudolph was lucky to still be at the crease after he was given a reprieve late on day three when the Umpire Decision Review System suggested enough of the ball had pitched outside the line of leg stump.
Rudolph made the most of that escape, getting himself set at the crease before lifting the tempo after the lunch break.
He slashed a cut shot through backward of point to move to 99 and swept Daniel Vettori to the square leg boundary to raise the milestone. The declaration came shortly after.
New Zealand suffered an early setback when Martin Guptill (6) was undone by a superb ball from Vernon Philander which nipped away and took the edge.
Rob Nicol weathered some torrid bowling and for 90mins battled hard to find his touch. He took the ball on the body and looked a bit like he was fending off over-sized wasps on his way to 19 from 71 balls.
But it was all for nothing with the right-handed hitting a full toss from Imran Tahir straight to Graeme Smith at mid-on. A shot which was the very definition of disappointing.
Scoreboard
South Africa first innings 238
New Zealand first innings 273
South Africa second innings (overnight 268-3)
A. Petersen c Southee b Bracewell 25
G. Smith b Bracewell 115
H. Amla c Guptill b Bracewell 2
J. Kallis c Nicol b Boult 113
J. Rudolph not out 105
AB de Villiers c McCullum b Williamson 29
M. Boucher not out 34
Extras (nb-3, w-1, lb-6, b-2) 12
Total (for five wickets dec, 140 overs) 435
Fall of wickets: 1-45 2-47 3-247 4-283 5-353
Bowling: Martin 23-4-74-0; Boult 26-4-93-1; Bracewell
25-3-70-3 (nb-3); Southee 26-4-100-0 (w-1); Vettori 32-5-65-0;
Nicol 1-0-9-0; Williamson 7-4-16-1
New Zealand second innings
R. Nicol c Smith b Tahir 19
M. Guptill c de Villiers b Philander 6
B. McCullum not out 58
R. Taylor not out 48
Extras (lb-2, w-2, nb-2) 6
Total (for two wickets, 41 overs) 137
Fall of wickets: 1-16 2-55
Bowling: Steyn 8-2-25-0 (w-1); Philander 12-2-29-1 (nb-2);
Morkel 7-2-27-0; Tahir 8-2-33-1; Kallis 6-1-21-0 (w-1)
New Zealand won the toss and opted to field
